Delay‐dependent decentralised H _∞ filtering for fuzzy interconnected systems with time‐varying delay based on Takagi–Sugeno fuzzy model

Abstract

This study focuses on the problem of delay-dependent H ∞ filter design for non-linear interconnected systems with time-varying delays via Takagi-Sugeno fuzzy models. Based on the delay-dependent fuzzy Lyapunov-Krasovskii functional and the fuzzy-free weighting matrix technique, the delay-dependent stability and a prescribed H ∞ performance index are guaranteed for the overall filtering-error system. In addition, a sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. Finally, two examples are given to demonstrate the effectiveness and advantage of the proposed approach.

New Decentralized $H_{\infty }$ Filter Design for Nonlinear Interconnected Systems Based on Takagi–Sugeno Fuzzy Models

“…Then, by the matrix decoupling technique similar to that in [13], a new delay-dependent H ∞ filter is designed in terms of linear matrix inequalities (LMIs). By contrast, our method produces less conservative results than the existing ones in [19] and [20]. Finally, two examples are given to illustrate the advantages and effectiveness of our results.…”

“…When the H ∞ filtering problem of interconnected systems is considered, the conventional centralized H ∞ design approaches developed in [12]- [17] are neither economically feasible nor necessary to nonlinear interconnected systems due to the complicated physical configuration and high dimensionality among them. Therefore, a decentralized H ∞ filtering approach is preferred in control design of large-scale interconnected systems because it attempts to avoid difficulties in the complexities of the design and debugging process, as stated in [18]- [20]. Moreover, in the fuzzy control design, the Takagi-Sugeno (T-S) fuzzy control and the adaptive fuzzy control [21], [22] are two main research directions.…”

“…Fuzzy controller designs for nonlinear multiple time-delay interconnected systems are provided in [29] and [30]. Furthermore, a new decentralized H ∞ filtering approach, that is, the local filters estimate the local output signals on the basis of the local measurements to guarantee the overall estimation performance and there is no information exchange between local filters, is developed for the filter design of fuzzy large-scale interconnected systems in [18]- [20].…”

“…The fuzzy weighting-dependent Lyapunov function approach depends on the upper bound for the time derivatives of membership functions which leads to limitations in practice while the fuzzy line-integral Lyapunov function approach is irrespective of such constraint on the derivatives of membership functions. Considering that time delay is inevitable in many practical control systems, the delay-independent decentralized fuzzy H ∞ filter design for nonlinear interconnected systems with multiple time delays is given in [19] and the delay-dependent case is provided in [20]. However, to the best of the authors' knowledge, there has been no result reported for the delaydependent decentralized H ∞ filter design of delayed fuzzy interconnected systems via the fuzzy line-integral approach, which motivates the present research.…”

Asynchronous Piecewise Output-Feedback Control for Large-Scale Fuzzy Systems via Distributed Event-Triggering Schemes

“…The works in [48], [49], [54], [55] studied the large-scale fuzzy systems with linear coupling A if instead of a general class of large-scale fuzzy systems with nonlinear coupling A if l in (1). Note that the control problem for largescale fuzzy systems with nonlinear coupling in (1) becomes more challenging than those with linear one available in [48], [49], [54], [55].…”