Robust stability and performance with fixed-order controllers

This paper deals with the problem of synthesizing or designing a feedback c ontroller of fixed dynamic order for a linear time-invariant plant for a fi xed plant, as well as for an uncertain family of plants containing paramete r uncertainty, so that stability, robust stability and robust performance a re attained. The desired closed-loop specifications considered here are giv en in terms of a target performance vector representing a desired closed-lo op design. In general, these point targets are unattainable with a fixed-or der controller. By enlarging the target from a fixed-point set to an interv al set the solvability conditions are relaxed and a solution is enabled. Re sults from the parametric robust control literature can be used to design t he interval target family so that the poles and zeros of the closed-loop sy stem are guaranteed to remain in a prescribed region of the complex plane, and closed-loop performance, measured for instance in the H-infinity norm a re attained, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach th at attempts to meet the desired closed-loop specifications. The approach de veloped here gives the entire set of controllers attaining the specificatio ns as a convex set and also can be recast to give the lowest-order controll er attaining specifications. (C) 1999 Elsevier Science Ltd. All rights rese rved.