Robust observer design in Markovian randomly switched linear systems

Abstract

This paper studies the problem of state estimation in randomly switched linear systems whose switching processes are Markov chains (MCs) and proposes observer design that can treat unobservable subsystems. Under certain structural conditions, this paper introduces a suitable design procedure for subsystems such that the estimation errors of the entire state converge to zero almost surely. The design procedure employs only the stationary distributions of the MCs. Robustness analysis and robust design of observers are further investigated when the stochastic information contains errors. This paper extends our earlier results on almost-sure convergence under independent and identically distributed switching processes or mean-square convergence under MCs, both without stochastic information uncertainty, to robust almost-sure convergence under MCs with uncertainty. Simulation case studies are used to demonstrate the observer design methods and their main properties.