H2 and H∞ dynamic output feedback control of continuous-time Markov systems with uncertain rates using LMIs

Abstract

The aim of this paper is to investigate the problems of H∞ and H2 dynamic output feedback control for continuous-time Markov jump linear systems (MJLS) subject to uncertain transition rates. Synthesis conditions are proposed in terms of parameter-dependent matrix inequalities with a scalar parameter and polynomial variables. The conditions become linear for fixed values of the scalar parameter, which provides an extra degree of freedom to search for feasible solutions and less conservative H∞ and H2 bounds. Differently from the existing approaches, the proposed method provides full order mode-dependent controllers constructed in terms of the state space matrices of the operation modes and partitions of the slack variables introduced in the design conditions. Therefore, the resulting controller does not depend explicitly on the Lyapunov matrix, being robust with respect to the uncertain transition rates. Moreover, the closed-loop MJLS stability and the bounds to the H∞ or H2 norm are certified by means of polynomially parameter-dependent Lyapunov matrices. Numerical examples illustrate the applicability and the advantages of the proposed technique when compared with other approaches from the literature.