New result on H∞ filtering for time-delay Markovian jump systems

This paper investigates the problem of H∞ filtering for continuous-time 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 solving the problem, we transform the system under consideration into an interconnected system. Based on the system transformation and the input-output approach, the stochastic stability of the original system is examined via the stochastic stability version of the scaled small gain theorem. 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 is also illustrated via numerical examples.