Quadratic Control of Linear Discrete-time Positive Systems

Abstract

The linear matrix inequalities approach is proposed to discrete-time linear positive system control design, mounting linear quadratic constraints into design conditions. Coupling together the set of linear matrix inequalities warranting the system positive structure, and the additional inequality guaranteing asymptotic stability of the controlled system, the design conditions are outlined to construct the positive closedloop scheme with a state-feedback positive control law gain. Some related properties are deduced to come towards a solution for forced-mode control policy in discrete-time linear positive system using the static decoupling principle. The proposed approaches are numerically illustrated.