A unified filter for singular Markovian jump systems with mixed delays based on an extended free‐matrix‐based inequality approach

Abstract

In this article, the problem of unified filters design including H ∞ , L 2 − L ∞ , passive, dissipative filters and their reduced-order ones is addressed for continuous-time singular Markovian jump systems with discrete and distributed delays. Unlike some existing works, the mixed delays can be fully captured by proposing an extended free-matrix-based integral inequality. By considering two cases of distributed delays, two novel criteria are presented to ensure the filtering error system to be stochastically admissible and extended dissipative. Some numerical examples are provided to illustrate the effectiveness of the unified filter design methods. K E Y W O R D S extended free-matrix-based integral inequality, singular Markovian jump systems, time-varying delays, unified filters

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

“…[4][5][6] In the past two decades, a large number of literatures on time-delay MJSs have been reported in the fields of filtering, estimation, control and so on. [7][8][9][10] On the other hand, fault is a serious threat to the system safety, which may cause huge losses if it occurs but cannot be detected in time. [11][12][13][14] Accordingly, a lot of studies about fault detection (FD) problems for time-delay MJSs with different characteristics have been developed.…”

“…Additionally, time‐delay is an inevitable phenomenon in many engineering systems that may cause performance degradations or even instability 4‐6 . In the past two decades, a large number of literatures on time‐delay MJSs have been reported in the fields of filtering, estimation, control and so on 7‐10 . On the other hand, fault is a serious threat to the system safety, which may cause huge losses if it occurs but cannot be detected in time 11‐14 .…”