Fixed-order controller synthesis for monotonic closed-loop responses: a linear programming approach

Abstract

We consider the problem of synthesizing dynamic controllers to guarantee monotonic closed-loop step responses. Restricting our attention to controllers which yield positive closed-loop systems, we derive synthesis conditions that are linear in the controller parameters. A linear programming formulation that attempts to optimize the decay rate of the closed-loop system while ensuring asymptotic stability and monotonic step response is developed. An alternative approach which guarantees closed-loop stability and a near-monotonic response is also introduced. Several illustrative examples demonstrate the effectiveness of the approach.