A general dynamic output feedback control for rectangular nonlinear discrete-time descriptor Markov jump systems

This paper studies the dynamic output feedback (DOF) control problem (CP) for rectangular discrete-time descriptor Markov jump systems (RDDMJSs) with Lipschitz nonlinear terms. There is no restriction on the relationship between the number of system equations and the dimensions of states. First, according to designing general DOF controllers, the resulted closed-loop systems are converted into square DMJSs (SDMJSs). Then, a novel sufficient condition is proposed in terms of linear matrix inequality (LMI) based on the stochastic Lyapunov theory, S-procedure and with free matrices, which guarantees the stochastic admissibility and the existence and uniqueness of solution of the closed-loop systems. Furthermore, by utilising the matrix decoupling technique (MDT) and introducing relaxation matrices, the controller design algorithm is given, and the general DOF controllers with free dimensions are designed. Last, two numerical examples and a practical application are provided to demonstrate the validity and superiority of the proposed methods.