$H_{\infty}$ Output Regulation for Discrete-Time Singular Markov Jump Systems Based on Extended State Observer

This paper investigates the $H_{\infty}$ output regulation problem for discrete-time singular Markov jump systems (SMJSs) based on extended state observer. Firstly, an extended state observer based full-order feedback controller is established. Sufficient conditions for the solvability of the output regulation problem and $H_{\infty}$ output regulation problem are provided. Then, the necessary and sufficient conditions for the existence of solutions to regulation equations are given based on Kronecker product and algebra condition. Furthermore, by certain matrix decoupling technology, a series of linear matrix inequalities (LMIs) are solved to design the observer and controller parameters matrices and minimize the $H_{\infty}$ norm. Finally, a numerical example is given to examine the reliability and validity of the proposed method.