Generalized guaranteed cost control with D-stability and multiple output constraints

This paper is concerned with the problem of robust generalized guaranteed cost control with D-stability and multiple output constraints for a class of linear uncertain systems. Being a combination of output performance indices, a generalized cost function is considered to the linear polytopic uncertain systems described in a unified framework. The aim is to design a state feedback controller, such that the closed-loop system is robust D-stable, and the upper bound of the generalized cost function is as small as possible subject to multiple output constraints. Based on parameter-dependent Lyapunov functions, convex conditions for the existence of such controllers are presented in terms of linear matrix inequality. The proposed approach shows a unified treatment of the linear systems in the differential, shift, and delta domains. Numerical examples are provided to illustrate the effectiveness of the design method.