M-matrix based robust stability and stabilization for uncertain discrete-time switched TS fuzzy systems with time-varying delays

Stability for IT2 T-S fuzzy systems under alternate event-triggered control

In this paper, an alternate event-triggered control is proposed to achieve stability of interval type-2 Takagi-Sugeno fuzzy systems. Comparing with the existing literature, this new control strategy displays an almost complete aperiodic feature which eliminates the conservativeness caused by time-triggered property of the traditional aperiodically intermittent control. Moreover, with two events being triggered alternately in this control strategy through examining two predetermined conditions, the efficiency of control can be further improved and the resources consumption can be greatly reduced. By employing the Lyapunov function and graph theory, several stability criteria are rigorously demonstrated. In addition, Zeno behavior is excluded in our system through obtaining a positive lower bound of the time interval between two triggering points. Subsequently, the validity of the presented strategy is evidenced by single-link robot arms systems. Finally, a numerical example is given to lend insight into the feasibility of our theoretical results.

Pole assignment stabilization for a class of switched nonlinear time-varying delay systems

This paper investigates the pole assignment stabilization with memory state feedback controllers for switched nonlinear time-varying delay systems. More general time-varying delays which depend on the subsystem number are considered. Based on novel common Lyapunov functions (CLFs), the aggregation techniques, the proprieties and the Borne-Gentina criterion, new algebraic stabilization criteria are established. The proposed design can guarantee the stability of the closed-loop systems under arbitrary switching. It allows to avoid researching a common Lyapunov function (CLF), considered a difficult matter. Four illustrate examples were finally utilized to exhibit the effectiveness of the obtained results.

Stability analysis and stabilization of discrete-time switched Takagi-Sugeno fuzzy systems

We endeavor to investigate the H_∞ synthesis problem of switched fuzzy systems composed by several discrete-time subsystems. By designing a novel QTD-MD Lyapunov function, novel criteria assuring stability as well as an expected H_∞ performance are first developed. Based on these sufficient conditions, some other conditions for solving the fuzzy H_∞ controllers are derived subsequently. Furthermore, the criteria are given as LMIs, thus the implementations are easy to execute. Simulations are also provided to confirm the feasibility of the presented strategy.

Extended dissipative filter design for T-S fuzzy systems with multiple time delays

This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H_∞, L₂ - L_∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H_∞, L₂ - L_∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.