LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.