Robust H ∞ control for singular systems with time-varying uncertainties

Abstract

In this paper, we investigate the problem of robust H ∞ control for singular systems with polytopic time-varying parameter uncertainties. By introducing the notion of generalized quadratic H ∞ performance, the relationship between the existence of a robust H ∞ dynamic state feedback controller and that of a robust H ∞ static state feedback controller is given. By using matrix inequalities, the existence conditions of robust H ∞ static state feedback and dynamic output feedback controllers are derived. Moreover, the design methods for such controllers are provided in terms of the solutions of matrix inequalities. An example is also presented to demonstrate the validity of the proposed methods.