Rehabilitative robotics, particularly lower-limb exoskeletons (LLEs), have gained increasing importance in aiding patients regain ambulatory functions. One of the challenges in making these systems effective is the implementation of an assist-as-needed (AAN) control strategy that intervenes only when the patient deviates from the correct movement pattern. Equally crucial is the need for the LLE to exhibit "transparency" — minimising its interaction forces with the wearer to feel as natural as possible. This paper introduces a novel approach to transparency control based on a human-in-the-loop velocity optimisation framework. The proposed method employs torque data captured from past steps through a Series Elastic Actuator (SEA) to approximate the wearer’s intended future movements and computes a corresponding transparent velocity trajectory. The velocity commands are complemented by an Adaptive Frequency Oscillator (AFO) based position controller that leverages the periodic nature of human gait and is modified with a force sensor for increased reactiveness to human gait variations. This approach is experimentally evaluated against a standard zero-torque controller with a stationary single-degree-of-freedom knee exoskeleton test platform in a proof-of-concept study. Preliminary results indicate that combining adaptive oscillators with interaction force sensing can improve transparency compared to the conventional zero-torque controller, using force readings for position control and torque measurements for velocity optimisation and control.

This article is concerned with the integrated design of fault estimation (FE) and fault-tolerant control (FTC) for uncertain nonlinear systems suffering from actuator faults and external disturbance. The uncertain nonlinear systems are characterized as the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, and IT2 membership functions are employed to effectively handle uncertainties. A fuzzy observer, utilizing only sampled-output measurements, is applied to simultaneously estimate actuator faults and system states. Based on the estimation, the fault-tolerant controller is designed to ensure the system stability under a predefined$H_{\infty}$performance. The sampling behavior complicates the system dynamics and makes the integrated FTC design more challenging. To confront this issue, the discontinuous Lyapunov functional technique is exploited to enhance stability results by considering the sampling characteristic, upon which FE and FTC units are co-designed in the linear matrix inequality (LMI) framework. To further relax stability criteria, the analysis process incorporates the bound information of membership functions through the membership-function-dependent (MFD) method. Additionally, the relationship of mismatched premise variables resulting from the sampling scheme is also taken into account. Moreover, considering the imperfect premise matching (IPM) framework, the proposed fault-tolerant controller provides greater flexibility in selecting the shapes of membership functions and number of fuzzy rules that can vary from the counterpart of the fuzzy system. Finally, the efficacy of the proposed FTC technique is validated through a detailed numerical example.

Conventional approaches to dietary assessment are primarily grounded in self-reporting methods or structured interviews conducted under the supervision of dietitians. These methods, however, are often subjective, inaccurate, and time-intensive. Although artificial intelligence (AI)-based solutions have been devised to automate the dietary assessment process, prior AI methodologies tackle dietary assessment in a fragmented landscape (e.g., merely recognizing food types or estimating portion size) and encounter challenges in their ability to generalize across a diverse range of food categories, dietary behaviors, and cultural contexts. Recently, the emergence of multimodal foundation models, such as GPT-4V, has exhibited transformative potential across a wide range of tasks in various research domains. These models have demonstrated remarkable generalist intelligence and accuracy, owing to their large-scale pre-training on broad datasets and substantially scaled model size. In this study, we explore the application of GPT-4V powering multimodal ChatGPT for dietary assessment, along with prompt engineering and passive monitoring techniques. We evaluated the proposed pipeline using a self-collected, semi free-living dietary intake dataset, captured through wearable cameras. Our findings reveal that GPT-4V excels in food detection under challenging conditions without any fine-tuning or adaptation using food-specific datasets. By guiding the model with specific language prompts (e.g., African cuisine), it shifts from recognizing common staples like rice and bread to accurately identifying regional dishes like banku and ugali. Another standout feature of GPT-4V is its contextual awareness. GPT-4V can leverage surrounding objects as scale references to deduce the portion sizes of food items, further facilitating the process of dietary assessment.

It is well-known that the tendon-driven robotic manipulator plays an important role in robotic-assisted minimally invasive surgery (MIS). However, due to the intrinsic nonlinearities, uncertainties, slack and hysteresis introduced by the tendon-driven actuation, the tendon-driven robotic manipulator is difficult to model and control when compared with the traditional actuation styles. To serve the modeling purpose, in this paper, the deep-learning-based intelligent modeling of inverse kinematics in the snake-like tendon-driven surgical instrument is presented. In the proposed approach the Deep Recurrent Neural Network (DRNN) with Long Short-Term Memory (LSTM) architecture is adopted to memorize and identify the nonlinear inverse kinematics of the tendon-driven surgical instrument through the history of the motor and tip positions. To collect highly reliable data to train the DRNN, the experiment to generate training data is carefully designed with the consideration of the stainless tendon characters and motor limitations. During the designed controller movements, the kinematics data is obtained by recording the motor positions and the tip positions. Besides, it is noticed that there are correlations of the sequential data samples, which could significantly reduce the modeling accuracy. To remove the correlations and improve the modeling performance, the correlations of the sequential data samples are removed by modifying the training processes. Modeling results and detailed discussions verified the effectiveness of the proposed approach.

In this work, the problem of tracking control for discrete-time nonlinear actuator-saturated systems via interval type-2 (IT2) T–S fuzzy framework is investigated. Improved on the (type-1) T–S fuzzy system, the IT2 T–S fuzzy system has a better capability for the expression of system uncertainty, and correspondingly, it will increase the difficulty of analysis, especially for the membership-functions-dependent (MFD) method. In addition, in this case, the control input nonlinearity caused by actuator saturation will complicate the stability analysis of the systems. We make an attempt to address the challenges that the information of membership functions (MFs) is underutilized or not utilized, by developing an MFD analysis approach, which allows the enhancement of design flexibility of IT2 fuzzy controller and effectiveness of lessening the conservativeness of the analysis result. The piecewise MFs which are formed by connecting the sample point on or close to the original IT2 MFs are utilized to approximate the original IT2 MFs, and the error between the piecewise MFs and the original upper and lower MFs is taken into account in the stability analysis. To acquire the linear matrix inequality-based (LMI-based) constraint, the actuator saturation is converted to a sector nonlinear issue.$\mathcal {H}_{\infty }$performance is considered to limit the difference between the reference system and the control saturated system. Examples are presented to illustrate the validity of the results.

Large AI models, or foundation models, are models recently emerging with massive scales both parameter-wise and data-wise, the magnitudes of which can reach beyond billions. Once pretrained, large AI models demonstrate impressive performance in various downstream tasks. A prime example is ChatGPT, whose capability has compelled people's imagination about the far-reaching influence that large AI models can have and their potential to transform different domains of our lives. In health informatics, the advent of large AI models has brought new paradigms for the design of methodologies. The scale of multi-modal data in the biomedical and health domain has been ever-expanding especially since the community embraced the era of deep learning, which provides the ground to develop, validate, and advance large AI models for breakthroughs in health-related areas. This article presents a comprehensive review of large AI models, from background to their applications. We identify seven key sectors in which large AI models are applicable and might have substantial influence, including: 1) bioinformatics; 2) medical diagnosis; 3) medical imaging; 4) medical informatics; 5) medical education; 6) public health; and 7) medical robotics. We examine their challenges, followed by a critical discussion about potential future directions and pitfalls of large AI models in transforming the field of health informatics.

Human-robot shared control, which integrates the advantages of both humans and robots, is an effective approach to facilitate efficient surgical operation. Learning from demonstration (LfD) techniques can be used to automate some of the surgical sub tasks for the construction of the shared control mechanism. However, a sufficient amount of data is required for the robot to learn the manoeuvres. Using a surgical simulator to collect data is a less resource-demanding approach. With sim-to-real adaptation, the manoeuvres learned from a simulator can be transferred to a physical robot. To this end, we propose a sim-to-real adaptation method to construct a human-robot shared control framework for robotic surgery. In this paper, a desired trajectory is generated from a simulator using LfD method, while dynamic motion primitives (DMP) is used to transfer the desired trajectory from the simulator to the physical robotic platform. Moreover, a role adaptation mechanism is developed such that the robot can adjust its role according to the surgical operation contexts predicted by a neural network model. The effectiveness of the proposed framework is validated on the da Vinci Research Kit (dVRK). Results of the user studies indicated that with the adaptive human-robot shared control framework, the path length of the remote controller, the total clutching number and the task completion time can be reduced significantly. The proposed method outperformed the traditional manual control via teleoperation.

dynamic output-feedback (DOF) controller for interval type-2 (IT2) T-S fuzzy systems with state delay. For nonlinear systems, the IT2 fuzzy model is an efficient modeling method which can better express uncertainties than the (type-1) fuzzy model. In addition, state delay is also a general factor that affects system performance. After analyzing the stability of the system, based on convex linearization and the projection theorem, this article proposes a delay-dependent output-feedback controller design method. The IT2 membership functions (MFs) of the fuzzy controller are chosen to be different from those of the model so as to increase the freedom of controller selection. A membership-function-dependent (MFD) method based on the staircase MFs is applied to relax the stability analysis results. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.

This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

This article focuses on the stability analysis and control design of an interval type-2 sampled-data fuzzy-model-based output-feedback (IT2SDFMBOF) tracking control system, which is formed by the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the stable reference model, and the interval type-2 sampled-data output-feedback (IT2SDOF) fuzzy controller. The design goal is to establish a proper IT2SDOF fuzzy controller that is able to drive the states of the nonlinear plant subject to uncertainties to track those of the stable reference model, and the$H_\infty$performance index is adopted to optimize the tracking control performance. To improve the robustness of the IT2SDOF fuzzy controller against uncertainties of the nonlinear plant, IT2 fuzzy sets are utilized. Considering that the tracking control system is sampled-data (SD) type, a two-sided looped-functional-based approach exploiting the information on the interval from time$t_k$to$t$and the interval from time$t$to$t_{k+1}$is applied to enhance the stability analysis. The imperfect premise matching (IPM) concept permits the number of rules and the premise membership functions of the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be different, which can be employed to promote the design flexibility. The tracking control system with the SD type and IPM design will cause the membership grades between the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be mismatched. In addition, the membership-function-dependent stability analysis approach that can introduce the boundary information of membership functions into the stability analysis is used to relax the stability conditions. The relaxed stability conditions subject to the$H_\infty$performance building on the Lyapunov stability theory are developed in terms of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed IT2SDFMBOF tracking control system.

Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the nonconvexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This article focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an$H_\infty$performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of nonconvex stability conditions, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a novel scalar implantation transformation technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static output-feedback tracking control with$H_\infty$performance being taken into account are obtained in terms of sum-of-squares. Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.

The system nonlinearity, sensor saturation, and the uncertainty will hamper the analysis and affect the control performance. Filtering is a signal processing method which facilitates the system analysis and synthesis by signal estimation or noise suppression. To achieve generalized filtering problem for nonlinear systems with sensor saturations with lower computational burden, this article addresses the reduced-order extended dissipative filter design for nonlinear sensor-saturated system which is modeled by interval type-2 (IT2) T–S fuzzy system. For IT2 T–S fuzzy systems, the main challenge exists in the acquisition of the information in IT2 membership functions (MFs) for analysis and design. A membership-function-dependent (MFD) method is applied to capture the information of the MFs for reducing the conservativeness introduced by MFs not involved in the analysis. An extended dissipative filtering method, under imperfect premise matching (IPM) concept that the membership functions of the filter are different from those of the model, is proposed for sensor-saturated IT2 fuzzy systems. The proposed method has a high flexibility in parameters adjustment of both the filter and the design condition, including extended dissipative matrices, approximation MFs, and sensor saturation degree, one can freely choose the parameters according to the required performance of the fuzzy filter. A numerical example is given to demonstrate the effectiveness of the results.

This article investigates the dissipativity-based filtering problem for the nonlinear systems subject to both uncertainties and time-varying delay in the time-delay interval type-2 (IT2) polynomial fuzzy framework. Filter design is a challenging issue for complex nonlinear systems especially when uncertainties and time delay exist. The IT2 polynomial fuzzy model is an effective and powerful approach to analyze and synthesize uncertain nonlinear systems. This is the first attempt to design both the full-order and reduced-order IT2 polynomial fuzzy filter to ensure that the filtering error system is asymptotically stable under the dissipativity constraint. The design of filtering is based on the imperfect premise matching scheme where the number of fuzzy rules and shapes of membership functions of the designed fuzzy filter can differ from those of the IT2 polynomial fuzzy model, to provide greater design flexibility and lower implementation burden. By utilizing the Lyapunov–Krasovskii-functional-based approach, the information of membership functions, time delay, and system states is taken into account in the design process to develop the relaxed membership-function-dependent and delay-dependent filtering existence criteria. Finally, simulation results are presented to illustrate the effectiveness of the filtering algorithm reported in this article.

The traditional master-slave teleoperation relies on human expertise without correction mechanisms, resulting in excessive physical and mental workloads. To address these issues, a co-pilot-in-the-loop control framework is investigated for cooperative teleoperation. A deep deterministic policy gradient (DDPG) based agent is realised to effectively restore the master operators' intents without prior knowledge on time delay. The proposed framework allows for introducing an operator (i.e., copilot) to generate commands at the slave side, whose weights are optimally assigned online through DDPG-based arbitration, thereby enhancing the command robustness in the case of possible human operational errors. With the help of interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy identification, force feedback can be reconstructed at the master side without a sense of delay, thus ensuring the telepresence performance in the force-sensor-free scenarios. Two experimental applications validate the effectiveness of the proposed framework.

Robotic dual-arm twisting is a common but very challenging task in both industrial production and daily services, as it often requires dexterous collaboration, a large scale of end-effector rotating, and good adaptivity for object manipulation. Meanwhile, safety and efficiency are primary concerns for robotic dual-arm coordinated manipulation. Thus, the normally adopted fully automated task execution approaches based on environmental perception and motion planning techniques are still inadequate and problematic for the arduous twisting tasks. To this end, this paper presents a novel strategy of the dual-arm coordinated control for twisting manipulation based on the combination of optimized motion planning for one arm and real-time telecontrol with human intelligence for the other. The analysis and simulation results showed it can achieve collision and singularity free for dual arms with enhanced dexterity, safety, and efficiency.

Highly nonlinear systems exist in many real-world applications. The control design of such systems is challenging even for existing advanced control theory. Besides, when there is uncertainty in the nonlinear system and networked control strategy is considered, the problem will become even more complicated. To confront the problem, for the first time, this article provides a solution for the tracking control design of the nonlinear networked control systems (NCSs) subject to uncertainty under the polynomial event-triggered mechanism (PETM). In the proposed tracking control scheme, the nonlinearity in the NCSs is effectively represented by a polynomial fuzzy model while the uncertainty is handled by the interval type-2 (IT2) fuzzy sets. The tracking control objective is to properly design the event-triggered IT2 polynomial controller, which drives the states of the plant to track those of the stable reference system under the PETM. Different from the existing works in the literature, the event-triggering condition can be varied according to the state to improve the flexibility and capacity of event-triggered mechanism. Furthermore, in some works reported in the literature, the perfect match of premise variables is assumed. However, this assumption is extremely difficult to be fulfilled in the event-triggered control applications. To address the long-standing challenge of an intrinsic mismatch issue of the premise variables due to event-triggering mechanism, in the proposed analysis, the imperfect premise matching (IPM) concept is adopted along with the membership-function-dependent (MFD) approach to facilitate the stability analysis and control synthesis. The stability conditions are summarized as sum-of-squares (SOS). The H∞index is utilized to evaluate the tracking control performance, and the performance can be improved through minimizing the H∞index. A detailed simulation example is provided to verify the effectiveness of the proposed method.

Limited by the operation time window and working space, space teleoperation tasks need to be completed within an expected time while ensuring that the end effector meets the physical constraints. Meanwhile, the interaction with unknown environments would cause uncertainty in the closed-loop system, which brings great challenges to the control design. To solve the above problems, the control performance issue for a class of space teleoperation systems subject to multiple constraints and interaction uncertainties is investigated in this article. The force interaction with the human operator/space environment is represented by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, where the uncertain equivalent mass and damping parameters can be effectively described and captured by IT2 membership functions. In order to reduce the communication burden and satisfy the constraints of settling time, transient-state performance and operating space, a time-varying threshold event-triggered control scheme together with exponential-type Lyapunov function is developed for the first time. We show that, with the proposed controller, the synchronization tracking errors are guaranteed to converge to a user-defined residual set within preassigned settling time, and never exceed the prescribed range despite unknown control direction and actuator faults, which solves the long-standing constraint issue with more flexibility due to the fact that the related constraints can be arbitrarily specific within the physically available range. Moreover, the convergence set is only dependent on fewer user-defined parameters rather than approximation errors, which provides an effective analysis technique to deal with the difficulty that the convergence accuracy is difficult to calculate quantitatively in the presence of unknown disturbance. Detailed simulation results are provided to show the effectiveness and merit of the proposed control strategy.

The articles in this special section are dedicated to the memory of Prof. Robert John, one of the pioneers of type-2 fuzzy sets and systems, who passed away during the preparation of this issue.

Accurately detecting tumors and estimating the depth of tumors is essential in the surgical removal of tumors. In robotic-assisted surgery, autonomous robotic palpation has the potential to provide more precise detection, tumors' depth estimation, and less intrusion when normal tissues surround tumors. In this article, by mimicking the human finger touch, we propose a tactile sensing-based deep recurrent neural network (DRNN) with long short-term memory (LSTM) architecture to improve the accuracy of the detection and depth estimation of tumors embedded in soft tissue. In the experimental setup, the hard inclusions simulate the tumors, while the phantom tissue is fabricated by silicon to simulate the soft tissue. During the experiment, the data from the force sensor and displacement of the robot palpation probe are for detection and depth estimation purposes. The collected sequential data set of the force and the displacement of the probe during one completed palpation process will go through the proposed DRNN network with deep LSTM architecture, in which the temporal dependencies of the sequential data will be captured in the cell states in the deep LSTM layers. Subsequently, the softmax classifier is adopted to determine if there is any hard inclusion exists and offer the depth estimation of the hard inclusions. Experiments based on 396 real data sets demonstrate that the detection accuracy for the testing data set is 99.2% and the depth estimation accuracy for the testing data set is 95.8%. The accuracy of the proposed method is best when comparing with other widely used methods. Note to Practitioners-The palpation of tumors motivated this article in the robot-assisted surgical systems through tactile feedback. In order to mimic the human touch on the soft tissue, this article presents a deep-learning-based approach to estimate the depth of the hard inclusions in the phantom tissue through force information. The displacement of the palpation probe and the touch force during one palpation are recorded as data sequences to train the deep model, which aims to capture dynamics and long-term dependence of the palpation process. In this article, we made the first successful attempt to accurately estimate the depth of the hard inclusions buried at different locations of the phantom tissue using only force information. The proposed approach can work in different robot-assisted scenarios, such as master-slave robotic surgery. In the clinic applications, the force sensor will be integrated at the end-effector of the robotic manipulator. According to the specific requirements, the force sensor and the robotic manipulator might be different from those used in this article. For some applications, such as the laparoscopic interventions, the complete vertical contact tends to be difficult to obtain due to the laparoscopic port effects. The projection of the recorded force data and displacement can obtain the information in the normal direction. The future work is going to be extended to tissue environments with arbitrary surface and tumors with various shapes/depths for more complex and prospective clinical applications.

In this paper, we investigate the stability and performance of the interval type-2 (IT2) polynomial fuzzy-model-based tracking control system, formed by an IT2 polynomial fuzzy model and an IT2 polynomial fuzzy controller, based on the output feedback and sampled-data structure. IT2 fuzzy sets are employed to capture the uncertainties of the nonlinear plant. Furthermore, considering the digital implementation of control strategy and only the system outputs are available, the IT2 polynomial fuzzy controller is of discrete time and output-feedback type. Both membership-function-independent and membership-function-dependent stability analysis, with the consideration of H∞performance index, are conducted to develop stability conditions in terms of sum-of-square based on Lyapunov stability theory. The information of membership functions, system states, and sampling process are included in the stability analysis for the relaxation of stability conditions. Simulation examples are presented to verify the effectiveness of the proposed tracking control approach.

In this article, the stability analysis and control synthesis of interval type-2 (IT2) polynomial-fuzzy-model-based networked control systems are investigated under the event-triggered control framework. The nonlinear dynamics in the plant is efficiently represented by an IT2 polynomial fuzzy model that the IT2 membership functions are utilized to capture the uncertainties in the plant. An event-triggered IT2 polynomial fuzzy controller is then designed to stabilize the nonlinear model subject to uncertainties. The stability conditions of the closed-loop control system are summarized in the form of sum-of-squares. Under the imperfectly premise matching (IPM) concept, the membership-function-dependent (MFD) approach is applied to endow the polynomial fuzzy controllers with more flexibility in terms of number of rules and premise membership functions. In the MFD approach under the IPM concept, both the number of rules and the shape of membership functions in the fuzzy models and controllers can be different. Also, the information of IT2 membership functions of the polynomial fuzzy model and controller is considered and adopted to further relax the stability conditions. Furthermore, the intrinsic mismatched issue of the premise variables of the fuzzy model and controllers due to the event-triggering mechanism is handled by the MFD approach. A detailed simulation example is provided to verify the effectiveness of the proposed event-based control strategy.

In this paper, the stability of polynomial-fuzzy-model-based (PFMB) systems equipped with mismatched interval type-2 (IT2) membership functions is investigated. Unlike the membership-function-independent methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own advantages, are proposed to conduct the stability analysis for the IT2 PFMB control systems. In the first one, we divide the operating domain into subdomains and then conduct the stability analysis incorporating the information and properties of the IT2 membership functions in subdomains. Through this approach, the stability conditions can be further relaxed compared with the membership-function-independent analysis. Polynomial functions are adopted in the second method to approximate the IT2 membership functions. The advantage of this method compared with the first one is that richer information of IT2 membership functions is considered without increasing the number of SOS conditions. In the third one, we combine the advantages of both the first and the second method offering a new approach which utilizes the information and properties of the lower and upper IT2 membership functions in subdomains through simpler polynomial approximation functions. It can be shown that more relaxed stability conditions can be obtained compared with the first two methods. Numerical examples and simulations are presented to verify the effectiveness of the proposed methods.