Minimax Optimal Control of Discrete-Time Uncertain Systems with Structured Uncertainty

In this paper we consider a guaranteed cost control problem for a class of uncertain discrete-time systems which contain structured uncertainties. The uncertainties are assumed to satisfy a certain sum quadratic constraint. The controller will be a minimax controller in the sense that it minimizes the maximum value of a cost function. For a given initial condition, the minimax optimal controller is constructed by solving a parameter dependent Riccati equation. This controller guarantees absolute stability of the closed loop system.