H_∞ control for linear systems with controller uncertainty

This paper is concerned with the problem of linear H_∞ controller design for linear time-invariant systems, in the presence of controller uncertainty. The controller to be designed is assumed to have time-varying, but norm-bounded additive uncertainties. Design methods are presented for both state feedback and dynamic output (measurement) feedback, both of which degenerate to the standard H_∞ state and output feedback control designs, respectively, when the controller uncertainties become zero. The designed controller with uncertainty is such that the closed-loop system is quadratically stable and has an H_∞ disturbance attenuation bound. The existence of solution to the standard H_∞ control problem guarantees the existence of such H_∞ controllers with a certain level of controller uncertainties. The generalization to uncertain plant is also considered. A numerical example are given to illustrate the design procedures and their effectiveness.