Optimal H2 Control for Uncertain Linear Systems

This paper proposes a method based on convex programming to calculate a guaranteed cost stabilizing state feedback control, for both continuous-time and discrete-time uncertain linear systems. In the uncertain case, it provides a guaranteed cost, i.e., an upper bound for the H2 norm of the closed-loop transfer function. In the absence of uncertainties, the numerical algorithm furnishes, under certain conditions, exactly the same optimal control gain obtained by the classical Linear Quadratic Problem. Thanks to the convexity of the proposed conditions, additional constraints can be easily taken into account as, for instance, robustness against actuators failure. Examples illustrate the theoretical results.