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Optimal output feedback control for discrete‐time Markov jump linear system with input delay and packet losses

This article investigates the optimal output feedback control problem for discrete‐time Markov jump linear system (MJLS) with input delay and packet losses in finite horizon. There are three main contributions. First, we assume that the state variable and the jump variable are available to the controller, and then we propose a new version of stochastic maximum principle. Based on the new proposed tool, an optimal state feedback controller is obtained by solving a set of delayed coupled difference Riccati equations. Second, under the condition that the state variable is unavailable to the controller, it is desired to design a dynamic Markovian jump controller such that the closed‐loop system minimizes the performance index. Thus, an optimal Markovian jump linear filter is proposed for MJLS with input delay and packet losses. Finally, based on the optimal filter, we prove that the separation principle holds for this case and then an optimal output feedback controller is presented. Some numerical examples are presented to illustrate the proposed approach.