Further result on H∞ filter design for continuous-time Markovian jump systems with time-varying delay

This paper investigates the problem of H∞ filtering for Markovian jump linear systems with time-varying delay. The aim of this problem is to design an H∞ filter that ensures stochastic stability of the filtering error system and a prescribed L2-induced gain from the noise signals to the estimation error, for all admissible uncertainties. For solving the problem, we transform the system under consideration into an interconnection system. Based on the system transformation and the stochastic scaled small gain theorem, stochastic stability of the original system is examined via the stochastic stability version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the stochastic scaled small gain theorem. The proposed H∞ filtering condition is demonstrated to be less conservative than most existing results. Moreover, the H∞ filter design condition is further presented via convex optimizations, whose effectiveness are also illustrated via numerical examples.