Finite‐frequency output feedback MPC for Markov jump systems

Abstract

AbstractThis paper investigates a general design framework of dynamic output feedback model predictive control (DOFMPC) for Markov jump systems within both time and frequency domain. Such a design with guaranteed H∞ and quadratic performance is formulated by a standard semi‐definite programming (SDP), and it is achieved by employing a special congruence transformation. The SDP condition greatly reduces the computational effort by eliminating bilinear matrix inequalities or equation constraints reported in existing references. Specifically, the H∞ norm of the transfer function is optimized within three types of frequency ranges on account of generalized Kalman–Yakubovic–Popov (GKYP) lemma. The quadratic index is optimized online via SDP. Finally, we verify the feasibility and effectiveness of the proposed method from both theoretical and practical point of view.