Decentralized $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ Filtering for Interconnected Markovian Jump Systems with Delays

Abstract

This paper deals with the problem of decentralized L 2 -L ∞ filtering for a class of interconnected (or large-scale) Markovian jump systems with constant time delays. The purpose is to present delay-dependent conditions for the existence of mode-dependent decentralized filters, which guarantees that the filtering error system is stochastically stable with a prescribed L 2 -L ∞ disturbance attenuation level. Such a purpose is achieved by using a mode-dependent centralized Lyapunov functional together with the so-called Jensen's inequality. The obtained synthesis conditions are expressed in terms of linear matrix inequalities (LMIs), which leads to a convex design method for the concerned filters. An example including numerical and simulation results is provided finally to illustrate the effectiveness of the proposed design method.