$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

Abstract

This paper considers the H ∞ filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e λt -weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e λt -weighted iISSiM and the H ∞ attenuation level from disturbance to estimation error is below a prescribed scalar. A set of sufficient conditions for the solvability of the H ∞ filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper.

Robust stabilisation for a class of stochastic T–S fuzzy descriptor systems via dynamic sliding‐mode control

“…For instance, in [29], the optimal guaranteed cost control was investigated; Zhao et al . [30] considered the problem of filtering; the passivity and passification problems were studied in [31].…”

Finite-time dissipative control of uncertain singular T–S fuzzy time-varying delay systems subject to actuator saturation

“…T-S fuzzy systems describe the nonlinear systems in the form of IF-THEN rules which utilize the fuzzy membership functions to represent the local linear input-output relations, such as Takagi and Sugeno (1985), Kumar et al (2018), Tian et al (2009), and Ge et al (2019). In the last 20 years, many studies have been conducted on the singular T-S fuzzy systems (Zhu and Xia 2014;Han et al 2012a, b;Su and Ye 2013;Zhao et al 2015; Han et al (2012a, b), and the less conservative conditions were given. designed a non-fragile static feedback controller for Markovian jump systems described by singular T-S fuzzy model.…”

Robust Stabilization of T–S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

“…This motivates introducing stochastic characteristics into the model representation. In recent years, many results have been reported on the study of T-S fuzzy stochastic descriptor systems, including passivity and passification [14], filtering [15], observer-based control [16] and guaranteed cost control [17]. Notice that in practice within control systems there always exist unknown disturbances and parameter uncertainties which increase the complexity of the system.…”