Finite‐time asynchronous dissipative filtering for Markovian jump systems with time‐varying delays and randomly occurred nonlinearity

Abstract

Summary The finite‐time dissipative filtering problem for time‐varying delayed Markovian jump systems with randomly occurred nonlinearity is addressed in this article. The modes of the desired filter are supposed to be asynchronous with the modes of the original system, which is more in line with the practical situation. The purpose of the problem under investigation is an asynchronous filter design which could make the error system finite‐time bounded as well as strictly dissipative. By constructing novel Lyapunov–Krasovskii functionals that covers the aforementioned two asynchronous modes and utilizing the theory of finite‐time analysis, some sufficient conditions are put forward to obtain the desired asynchronous filter by virtue of the linear matrix inequalities approach. A numerical example and a tunnel diode circuit are finally provided to demonstrate the effectiveness of our proposed method.

Finite‐time composite control for fuzzy delayed semi‐Markovian jump systems with multiple disturbances and uncertainty

“…MJSs have been widely applied in various fields. [3][4][5] On the basis of MJSs research, scholars began to focus on the semi-Markovian jump systems (S-MJSs) which has lower conservatism. P. Levy proposed the semi-Markov model in 1954, but it was not until the S-MJSs was proposed that this model began to be widely valued.…”

“…MJSs are random switching systems which can model real physical object with multiple modes characteristics. MJSs have been widely applied in various fields 3‐5 . On the basis of MJSs research, scholars began to focus on the semi‐Markovian jump systems (S‐MJSs) which has lower conservatism.…”

Dissipative fault detection for time‐delay nonlinear Markov jump systems with measurement outliers under stochastic communication protocol

“…It is worth noting that dissipativity can be regarded as a more general performance index, which includes H ∞ and passivity performance. 43,44 Up to now, some scholars have investigated the dissipative FD issues for MJSs. 45,46 For instance, the asynchronous dissipativity-based FD scheme has been proposed for T-S fuzzy MJSs with data dropouts in Reference 45, in which an FD filter based on hidden Markov model has been designed.…”

“…In the FD studies mentioned above, the augmented FD system has been required to meet $$$ {H}_{\infty } $$$ performance. It is worth noting that dissipativity can be regarded as a more general performance index, which includes $$$ {H}_{\infty } $$$ and passivity performance 43,44 . Up to now, some scholars have investigated the dissipative FD issues for MJSs 45,46 .…”