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

This paper discusses the problem of mixed
$H_{\infty }$
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
$H_{\infty }$
performance. Finally, a tunnel diode example in elaborated to show the effectiveness of our proposed method.