This article is concerned with the problem of functional observer-controller (FOC) design when a complex unmeasurable premise variable (UPV) exists in the Takagi-Sugeno (T-S) fuzzy systems. Considering the nonlinearities in the UPV, a new transformation method is designed to linearize the premise variable (PV). Then, the PV could be estimated through the proposed FOC. The observer and controller gains are derived by deducing convex robust and stability conditions. Furthermore, a robust separation principle is utilized to make the estimate and control error system stable. Finally, simulation examples are provided to illustrate the effectiveness of the proposed method.

To address the problem of robust stability analysis for interval type-2 fuzzy systems (IT2FSs), this paper proposes an innovative analysis approach based on model transformation. Firstly, a classical piecewise linear approximation method is utilized to process the upper boundary membership functions (UMFs) and lower boundary membership functions (LMFs) of the footprint of uncertainty (FOU) in IT2FSs, resulting in linear boundary membership functions (MFs) that are more convenient for analysis, along with the corresponding approximation error functions. Subsequently, a novel error model transformation method is introduced to handle these error terms. By constructing new fuzzy rules and MFs, the boundary error terms are converted into a new fuzzy model, thereby incorporating more information about the error functions into the stability analysis. Based on this model, a robust stability condition in the form of linear matrix inequalities (LMIs) are derived, achieving improved robustness. Finally, the effectiveness of the proposed method is validated through simulations on real-world systems, and its superiority is demonstrated by comparison with existing methods.

This article addresses the problem of dynamic event-triggered (DET) control for networked interval type-2 (IT2) fuzzy systems subject to multiple cyber-attacks, which contain deception attacks and aperiodic denial-of-service attacks simultaneously. First, a multiple cyber-attack model is established for the IT2 fuzzy systems with multiple cyber-attacks and external disturbances. Second, an improved DET mechanism (DETM) is proposed to reduce the communication burden. Contrasting with existing works, by introducing two adjustable parameters into the novel DETM, the presented DETM has more flexibility in adjusting the data packet transmissions to conserve more limited network resources. Meanwhile, the Zeno behavior is probably excluded under the proposed DETM while preserving the system performance. Third, imperfectly matched membership functions (MFs) are considered between fuzzy controller and IT2 fuzzy model, and the global boundary information of MFs and slack matrices are introduced to relax stability conditions. Besides, by constructing a proper Lyapunov–Krasovskii functional, sufficient conditions are obtained to ensure the exponentially mean-square stable of the IT2 fuzzy systems with the$H_{\infty }$performance. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.

For the conservatism issue of state-feedback control for Takagi–Sugeno (T–S) fuzzy systems, a novel local controller design method and stability analysis approach are proposed in this article. First, based on a membership function piecewise linearization technique, a local linear controller is proposed to form a closed-loop system. Then, a series of system stability conditions are derived using quadratic and piecewise function approaches. Further, with a designed fuzzy local controller and fuzzy Lyapunov function, less conservative stability conditions are obtained. Finally, a simulation example is adopted to make comparisons with existing and proposed methods. The results clearly show the conservatism reduction and excellent performance of the proposed approach.

For the output feedback control problem of a Takagi-Sugeno (T-S) fuzzy system with unknown premise variables (UPV) and external disturbances, a new observer-based controller H∞robust synthesis approach is proposed. To utilize the membership functions more effectively, in this article, a membership functions constructed vector is used as new premise variables. Then, the error items which are induced by UPV are decoupled into a new T-S fuzzy system. For the derived stability and robustness conditions in complex bilinear matrix inequality form, more relaxed sufficient conditions which can be solved directly by convex optimization method are proposed. Finally, a suspended floater control system based simulation process is carried out. The conservatism reduction effects among traditional and decoupling approaches are given, the state estimation effects of the observer and control performances are also verified.

For the stability analysis of a polynomial fuzzy system, a new polynomial membership function approach is proposed to reduce conservatism. In this article, based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system. Then, the membership-function-dependent polynomial-based stability conditions are derived. The obtained polynomial membership functions and approximation errors will be involved in the stability analysis process. Based on the sum-of-squares optimization technique, polynomial conditions can be directly solved. Finally, by several numerical and practical examples, conservatism reduction effects are shown by comparisons with existing methods.

The observer-based controller design for a T-Sfuzzy system subject to external disturbance is investigated in this paper. First, an H∞ observer is designed to estimate the unknown system states, by a transformation process for system states and the disturbance term, a state feedback H∞ controller is given. Then, the separation principle for a T-S fuzzy system subject to external disturbance is proposed. With the help of the improved separation principle, the observer and controller can be combined together to make the fuzzy system input-state stable, while the H∞ index can also be guaranteed. The proposed design approach is applicable for both known and unknown premise variables. In stability analysis, the membership functions derivatives dependent method is proposed to reduce the conservatism. In the simulation part, stability analysis of a three-rule system is carried out to illustrate the conservatism reduction effects in Example 1; then, a vessel dynamic positioning control process subject to ocean disturbance is adopted to illustrate the effectiveness of the proposed methods for both known/unknown premise variable cases.

A class of nonlinear systems with external disturbances and noise are studied, where the state of the system cannot be measured. A controller is designed by using the estimated state with an observer such that the states of the closed-loop system track the states of a given reference model, and meet a given H performance, at the same time attenuate disturbance and satisfy a guaranteed cost upper bound J*c. Finally, a simulation example is given to verify the effectiveness of the proposed theory.