A new design of H∞ filtering for continuous-time Markovian jump systems with time-varying delay and partially accessible mode information

• Published in: Signal processing Vol. 93; no. 9; pp. 2392 - 2407
• Main Authors: Wei, Yanling, Qiu, Jianbin, Reza Karimi, Hamid, Wang, Mao
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2013; Elsevier
• Subjects: [formula omitted] filtering; Applied sciences; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Markovian jump system; Partially accessible mode information; Scaled small gain theorem; Signal and communications theory; Signal, noise; Telecommunications and information theory; Time-varying delay; Markovian jump system; Time-varying delay; H∞ filtering; Partially accessible mode information; Scaled small gain theorem; Markov process; Filtering; Probabilistic approach; H infinite control; Feedback regulation; H; Continuous time; Delay system; Markov model; Stochastic process; Time variation; Linear system; Simulation; Interconnection; Linear matrix inequality; Signal processing; Delay time; Reduced order model; Linearization
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.02.014

In this paper, the delay-dependent H∞ filtering problem for a class of continuous-time Markovian jump linear systems with time-varying delay and partially accessible mode information is investigated by an indirect approach. The generality lies in that the systems under consideration are subject to a Markov stochastic process with exactly known and partially unknown transition rates. By utilizing the model transformation idea, an input–output approach is employed to transform the time-delayed filtering error system into a feedback interconnection formulation. Invoking the results from the scaled small gain theorem, an improved version of bounded real lemma is obtained based on a Markovian Lyapunov–Krasovskii functional. The underlying full-order and reduced-order H∞ filtering synthesis problems are formulated by a linearization technique. Via solving a set of linear matrix inequalities, the desired filters can therefore be constructed. The results developed in this paper are less conservative than existing ones in the literature, which are illustrated by two simulation examples.