Robust L₂ − L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process

Abstract

This paper investigates the problem of robust L₂ − L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robust L₂ − L∞ filter is designed which guarantees that the resulting error dynamic system is robustly stochastically stable and satisfies a prescribed L₂ − L∞ performance index. A numerical example is given to illustrate the effectiveness of the developed techniques.