The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions . Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

The aim of this study is to investigate less conservative conditions for a parameterized linear matrix inequality (PLMI) expressed in the form of a double convex sum. This type of PLMI frequently appears in Takagi–Sugeno (T–S) fuzzy control system analysis and design problems. In this letter, we derive new less conservative linear matrix inequalities (LMIs) for the PLMI by employing the proposed sum relaxation method based on Young's inequality. The derived LMIs are proven to be less conservative than the existing conditions related to this topic in the literature. The proposed technique is applicable to various stability analysis and control design problems for T–S fuzzy systems, which are formulated as solving the PLMIs in the form of a double convex sum. Furthermore, examples are provided to illustrate the reduced conservatism of the derived LMIs.

This paper addresses the problems of local stability analysis, local stabilization, and computation of invariant subsets of the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems. Improvements on the existing stability and stabilization conditions are achieved through the reduction of conservatism. To release the conservatism further, the so-called multidimensional fuzzy summation approach is adopted. The design and analysis conditions are expressed as one-parameter minimization problems which can be solved via a sequence of linear matrix inequality optimizations or treated as eigenvalue problems. Examples are given to show the validity of the proposed method.

This paper addresses stabilization problems for a nonlinear system via a sampled-data fuzzy controller. The nonlinear system is assumed to be exactly modeled in Takagi-Sugeno's form, at least locally. Unlike the conventional direct discrete-time design approach based on an approximate discrete-time model, the sampled-data fuzzy controllers are designed based on an exact discrete-time model. Sufficient design conditions are formulated in terms of linear matrix inequalities. It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system. A numerical example is given to illustrate the effectiveness of the proposed methodology.

In this paper, we present an autonomous in-pipe robot navigating system using vision-based landmark recognition. We propose to use special features of the pipelines (such as elbows or branches) as landmarks by recognizing the shadows of the elbows and branches. To obtain consistent shadow images, the in-pipe robot equips with specially designed illuminator. By analyzing the shadow, the robot can easily identify these landmarks, detect the direction of the passage, and adaptively traverse through while continuously updating the map. The effectiveness of the proposed method is verified by real experiments using the in-pipe robot MRINSPECT V for inspecting inside of the miniature urban 8-inch gas pipeline structure.

Takagi-Sugeno (T--S) fuzzy-model-based static output-feedback controller design is a challenging issue due to the nonconvexity in the Lyapunov stability condition. Recently, a convexified linear matrix inequality (LMI) condition was proposed for the problem by additionally importing as many equality constraints as the number of the fuzzy rules with a variable in the paper from the study of Fanget al. However, numerical experiences seem to imply the infeasibility of the proposed LMI. This letter shows that their LMI problem may be feasible.

In this paper we present an in-pipe robot, called MRINSPECT V (Multifunctional Robotic crawler for In-pipe inSPECTion V), which is under development for the inspection of pipelines with a nominal 8-inch inside diameter. To travel freely in every pipeline element, the robot adopts a differential driving mechanism that we have developed. Furthermore, by introducing clutches in transmitting driving power to the wheels, MRINSPECT V is able to select the suitable driving method according to the shape of the pipeline and save the energy to drive in pipelines. The robot aiming for autonomous navigation is configured with four modules serially connected. Two active driving modules are located in front and rear of the system, respectively. Passive modules are linked between the driving modules. This module-based robot can fit to narrow and winding pipelines by using the novel mechanism such as the specially designed module-joints. In this paper, the critical points in the design and construction of the proposed robot are described with the preliminary results of experiments that yield good mobility and increased efficiency.