Dissipative analysis and control for discrete-time state-space symmetric systems

In this paper, the problem of dissipativity analysis and output feedback control synthesis for discrete linear time-invariant systems with state-space symmetry is investigated. Firstly, an explicit expression of H_∞ norm for discrete-time symmetric system is given under the mixed H_∞ and positive real performance criterion, and this is a particular case of dissipative systems. Subsequently, we consider the control synthesis problems for such systems and obtain an explicit parameterized expression of the static output feedback controllers. Finally, two numerical examples are employed to show the effectiveness and reliableness of the proposed approach.