ABSTRACT
This paper presents a new technique for designing H ∞, controllers for systems with time-varying parameter uncertainty. More precisely, the proposed technique allows us to design linear dynamic output feedback controllers which guarantee both robust stability and some prescribed H ∞ performance of the closed-loop system. Our results are based on the notion of quadratic stability with disturbance attenuation with which an equivalence is established between the robust H ∞ control problem and a scaled H ∞ control problem. In light of existing results on H ∞ control, an algebraic Ricatti equation approach is used to characterize the robust H ∞ controllers and the “worst case” parameter uncertainty. We have also applied the technique to the problem of quadratic stabilization via dynamic output feedback and the problem of H ∞ control for systems with block-diagonal time-varying uncertainty. The results of this paper are analogous to those in the μ-synthesis developed for time-invariant complex uncertainty and can be viewed as a version of the μ-synthesis for time-varying parameter uncertainty.
