Stabilization and H∞ control of continuous-time symmetric systems

In this paper we address the H-infinity control analysis, the output feedback stabilization, and the output feedback H-infinity control synthesis problems 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 feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state-space symmetric systems. For the H-infinity control synthesis problem we derive an explicit expression for the optimally achievable closed-loop H-infinity norm and the optimal control gains. Extension to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequality formulations of the stabilization and the H-infinity control synthesis problems using simple matrix algebraic tools.