Dynamic Output-Feedback Control for Markov Linear Parameter-Varying Systems

Abstract

This paper addresses the problem of gain-scheduled $H_{\infty } $ dynamic output-feedback control for Markov linear parameter-varying systems. Unlike most existing results that assume bounded parameter variation rates, a switching approach is designed to handle the time derivative of the Lyapunov matrix, allowing arbitrarily large or unknown parameter variations. The corresponding controller employs gain matrices with nonlinear dependence on the uncertain parameters, improving modeling flexibility. Furthermore, two novel parameter-dependent Lyapunov functions are proposed to reduce conservatism. The first exhibits nonlinear dependence on the uncertain parameters and adopts a full-block structure, in which both the Lyapunov matrix and its inverse are partitioned into four submatrices: the first diagonal block depends linearly on the uncertain parameters, while the remaining blocks depend nonlinearly or are parameter-independent. The second Lyapunov function depends linearly on the parameters and employs the elimination lemma with slack matrices to decouple the Lyapunov matrix from the closed-loop system. Finally, three numerical examples demonstrate the effectiveness and superiority of the proposed method. Note to Practitioners—Markov linear parameter-varying (LPV) systems arise in a wide range of engineering applications, including aerospace and automotive systems with multiple operating modes, networked control systems, and electromechanical systems. For gain-scheduled output-feedback control of Markov LPV systems, most existing approaches rely on the assumption that the scheduling parameters vary with known bounded rates. However, in practical applications, scheduling parameters are often generated by external operating conditions, load variations, or estimation mechanisms, whose variation rates are difficult to characterize a priori and may exhibit rapid or abrupt changes. To address this issue, this paper develops a gain-scheduled dynamic output-feedback control method for Markov LPV systems by introducing a switching method to handle the time derivative of the parameter-dependent Lyapunov matrices, and this design removes the need for any prior constraints on parameter variation rates while guaranteeing exponentially mean-square stability and $H_{\infty } $ performance.