Stabilization and H-infinity control of symmetric systems: an explicit solution

In this paper we address the H-infinity control analysis, the output feedba ck stabilization, and the output feedback H-infinity control synthesis prob lems for state-space symmetric systems. Using a particular solution of the Bounded Real Lemma for an open-loop symmetric system we obtain an explicit expression to compute the H-infinity norm of the system. For the output fee dback stabilization problem we obtain an explicit parametrization of all as ymptotically stabilizing control gains of state-space symmetric systems. Fo r the H-infinity control synthesis problem we derive an explicit expression for the optimally achievable closed-loop H-infinity norm and the optimal c ontrol gains. Extension to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequ ality formulations of the stabilization and the H-infinity control synthesi s problems using simple matrix algebraic tools. (C) 2001 Elsevier Science B .V. All rights reserved.