Constrained Control of Continuous Positive Systems with Uncertain Parameters

A robust stabilization method is proposed for a class of uncertain continuous positive systems with bounded inputs and states. First, based on the analysis of Metzler matrix properties, necessary and sufficient conditions are established to guarantee that systems are positive and states are bounded. Based on the stability theories of positive systems, a further necessary and sufficient condition is delivered to ensure the asymptotical stabilities of the system. Furthermore, under the bounds on inputs and states, a robust state feedback controller is designed for linear programming methods. Simulation examples illustrate the effectiveness of the proposed algorithm.