Design Constraints in the Synthesis of Control of Positive Linear Discrete-time Systems

The linear matrix inequality approach is proposed to state control design of discrete-time linear positive systems, guaranteeing the closed-loop system positiveness, enabling attenuation of the impact of disturbances on the system and, if it is necessary, also giving possibility to mount limiting quadratic constraints on state variables into design conditions. Constructing the set of linear matrix inequalities warranting the strictly positive structure and the Lyapunov inequality forcing quadratic stability of the controlled system, the design conditions outlined and proven are the main results of the paper. The diagonal stabilizability had to be included into the set of linear matrix inequalities to construct the closed-loop schemes with a positive control law gain. The proposed approach is numerically illustrated.