Quadratic Stabilization by H^∞ State Feedback Control with Adjustable Parameter

Abstract

A new quadratically stabilizing state feedback controller is derived based on the parameterization of H^∞ controllers. The controller contains a contractive time-varying gain. The time-varying gain can be used to adjust the responses of the resulting closed-loop system. As one of the methods of using this adjustable gain, we consider a steepest descent tuning of Lyapunov functions. Particularly, this tuning method is also a new gain-scheduled control design when parameter variations are assumed to be available for feedback control