Adaptive Event-Triggered Mixed $H_{\infty}$ and Passivity-Based Filter Design for Nonlinear T-S Fuzzy Markovian Switching Systems With Time-Varying Delays

Abstract

This paper discusses the problem of mixed H ∞ and passivity-based filter design for non-linear T-S Fuzzy Markovian Switching Systems (F-MSSs) with time-varying delays, under the adaptive event-triggered scheme. At first, an adaptive event-triggered scheme (AET-S) is put forward, that adjusts the communication threshold level, in an adaptive manner, in order to mitigate the effect of the communication burden. Second, the filter design problem is solved with the communication delays in terms of linear matrix inequalities (LMIs), by considering a novel Fuzzy-Markovian Lyapunov-Krasovskii functional (FMLKF) containing mode-dependent integral terms such that the resulting filtering error system is stable with the desired H ∞ performance. Finally, a tunnel diode example in elaborated to show the effectiveness of our proposed method. INDEX TERMS Fuzzy-Markovian switching systems (F-MSSs), adaptive event-triggered (AET) scheme, fuzzy markovian Lyapunov-Krasovskii functionals, delayed fuzzy filters.

Fault Detection Filter Design of Polytopic Uncertain Continuous-Time Singular Markovian Jump Systems with Time-Varying Delays

“…erefore, according to [35][36][37][38], the unforced input system (9) has a unique impulse-free solution for all t ≥ 0 when Assumption 1 holds. Before proceeding to the next step, we introduce the following important definitions to drive our main results.…”

“…Additionally, it has been shown that time-varying delays are universal in real applications because of the signal transmission in communication, and it can lead to systems performance degradation and instability [34][35][36][37][38]. Inevitably, time delays also exist in SMJSs, and it is necessary to investigate the SMJSs with time-varying delays.…”

Quantized Dissipative Observer-Based Output Feedback Control for a Class of Markovian Descriptor Jump Systems with Communication Delay

“…Definition 2 (see [19,53]). Consider matrices Θ ≥ 0, Φ 1 ≤ 0, and Φ 2 and Φ 3 > 0, which fulfill (‖Φ 1 ‖ + ‖Φ 2 ‖)‖Θ‖ � 0. en, we can say that system (18) is to be extended dissipative if there exists a scalar ρ such that the following inequality holds for any t f ≥ 0 and all ω(t) ∈ L 2 [0, ∞]:…”

“…Let F be the weak infinitesimal generator of the random process x t , r t . en, by implementing similar techniques to those in [53], we have that, for r t � i ∈ S,…”

Event-Triggered Dissipative Filter Design for Semi-Markovian Jump Systems with Time-Varying Delays

“…As a result, the unnecessary communication resources are saved in the event-triggered scheme. In recent years, the event-triggered scheme has been utilized in the controller and filter design problem for various dynamic systems [31][32][33][34][35][36]. As for SMJSs, the event-triggered leader-following consensus for a multiagent system with semi-Markovian jumping parameters was studied in [37].…”