Robust H∞ control for uncertain discrete-time systems with circular pole constraints

Abstract

This paper investigates the problem of robust H ∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H ∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H ∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H ∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H ∞ control and robust pole assignment of uncertain systems.