Control Design for a Class of Uncertain Discrete-time Positive Time-delay Linear Systems

For linear uncertain positive time-delay discrete-time systems this paper proposes an extended way to reflect structural system parameter constraints and positiveness when solving the problem of quadratic stability. A new observation is proposed in the form of linear matrix inequalities to guarantee the system parameter constraint representation, the closed-loop strictly positiveness and quadratic stability. Moreover, only time-invariant strictly positive control law gains are used in the feedback loop. Closely connected to the obtained results is the fact that the impact of positive system matrix structures is successfully implemented. The results are transparent in the considered case and the numerical example assess the task feasibility.