Stabilization and H∞ control of discrete-time symmetric systems

We examine the H∞ control analysis, the output feedback stabilization, and the output feedback H∞ control synthesis problems for discrete-time state-space symmetric systems. We obtain explicit analytical solutions for the H∞ norm of such systems, and an explicit parametrization of the output feedback stabilizing controllers and H∞ controllers. Extensions 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∞ control synthesis problems for discrete-time systems using simple matrix algebraic tools. The results have obvious computational advantages, especially for large scale symmetric systems.