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

In this paper, the delay-dependent H∞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∞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.