Design of static output-feedback controller for uncertain discrete time systems with positivity constraint on closed-loop system and control signal

This paper studies the linear positive discrete-time systems with the uncertainty in the system model. Some parameters of system’s matrix are unknown and only some information about their lower and upper bounds are available. The goal of this paper is design of output feedback control law in the presence of parametric uncertainties. The control law is designed in a way that in addition to asymptotic stability of the closed-loop system; it guarantees the positivity of the closed-loop system which adds some complexity in the process of problem solving. Another case has also been investigated in this paper is design of output feedback control law such that as well as the asymptotic stability and positivity of the closed-loop system; the control signal be also positive. The realization of this constraint is necessary in some positive systems. In this paper, two theorems are given and proved. Moreover, the conditions expressed in these theorems are converted to linear programming formats. Finally, computer simulations are presented to verify the theoretical results.