Static Output Feedback Controller Design for Constrained MIMO Discrete-Time Positive System

This paper is concerned with synthesis problems for constrained multi-input multi-output (MIMO) discrete-time linear positive systems. First, the stabilization problem by taking static output feedback controller has been solved. The designed controller ensure the positivity and the asymptotic stability of the unconstrained closed-loop system. More precisely, necessary and sufficient conditions on the existence of such controller are established, and the desired gain matrix can be calculated easily through the solution of the proposed linear programming (LP) problem. Furthermore, MIMO discrete-time linear positive systems with constraints on the control inputs, or on the state variables are considered. For such systems, different constrained stabilization problems are formulated when static output feedback controller is used. Moreover, it is shown that these problems are solvable in terms of LP problems. In addition, we show how the obtained results can be extended to maximize the domain of attraction of the constrained discrete-time positive system. Finally, theoretical results are supported by a numerical simulation, and also by an application to certain pests dynamic process.