QUADRATIC STABILIZABILITY OF LINEAR UNCERTAIN SYSTEMS WITH PRESCRIBED H ∞ NORM BOUNDS

Abstract This paper presents a method to synthesize a linear state feedback control for dynamic continuous-time linear systems. The major improvement is that the method takes into account, as a design requirement, an upper bound to the H∞ norm of a specified closed-loop transfer function. The condition that guarantees the H∞ norm bound, giving the linear state feedback gain, has convexity properties that allow the controller design to be applied to uncertain systems with convex-bounded uncertainties. Therefore, using the state space models and Lyapunov conditions, the method solves jointly both quadratic stabilizability and H∞ control problems.