Dissipative Approach in Control Design for Linear Discrete-time Positive Systems

The linear matrix inequalities formulation is proposed to discrete-time linear positive system control design, mounting system matrix structure 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 closed-loop scheme with a state-feedback positive control law gain. Using the proposed method, the closed-loop system state, after reaching it, remains in an ellipsoidal positively invariant set. The proposed approach is numerically illustrated.