H∞ filter design for time-delay Markovian jump systems

This paper investigates the H∞ filtering problem for discrete time-delay Markovian jump systems with application to networked control systems. To design a full-order filter which ensures the stochastic stability and a prescribed H∞ performance level for the filtering error system, the Scaled Small Gain (SSG) Theorem is developed for stochastic systems. By employing a two-term approximation to delayed state variables, the original system is transformed into an input-output form consisting of two subsystems. Based on the developed SSG Theorem and the proposed Lyapunov-Krasovskii Functional (LKF), the scaled small gains of the subsystems are analyzed to establish a new condition for the existence of the H∞ filters. In addition, the corresponding H∞ filter design scheme is proposed. Finally, a numerical example is presented to demonstrate effectiveness of the designed H∞ filters.