Unified filters design for singular Markovian jump systems with time-varying delays

Abstract

This paper considers the problem of unified mode-dependent and mode-independent filters design for continuous-time singular systems with Markovian jumping parameters and time-varying delays. The main objective of this paper is to design the L2−L∞, H∞, passivity, strict (Q, S, R)-dissipativity, very-strict passivity filters in a unified framework so as to ensure that the filter error system is stochastically admissible and extended dissipative. By tuning the weighting matrices, the extended dissipativity performance can reduce to the L2−L∞ performance, H∞ performance, passivity, strict (Q, S, R)-dissipativity and very-strict passivity, respectively. A mode-dependent and delay-dependent stochastic Lyapunov–Krasovskii functional is proposed to reflect the information of Markovian jump modes and the time-varying delays, and a set of linear matrix inequalities (LMIs) are utilized to derive sufficient conditions which guarantee that the desired unified filters can be constructed. Three numerical examples including an oil catalytic cracking process (OCCP) are employed to verify the usefulness and effectiveness of the main results obtained.