On the dissipative analysis and control of state-space symmetric systems

This paper addresses the quadratic dissipativity analysis and static output feedback control of linear time-invariant systems which are state-space symmetric. By considering particular weighting matrices, we present a necessary and sufficient inequality condition for checking asymptotic stability and quadratic dissipativity for this class of systems. Our analysis condition involves only system state matrices and known weighting matrices. Therefore, this condition is easy to check numerically and particularly suitable in the case of large-scale symmetric systems. The application of our analysis result to symmetric static output feedback (SSOF) control design is also reported in this paper. An easily tractable numerically, necessary and sufficient condition for the existence of a SSOF control law and an explicit parametrization of all SSOF controllers guaranteeing the asymptotic stability and the quadratic dissipativity of the closed-loop system is given. Note that the results presented in this paper generalize some results already proposed in the literature to a more general case of quadratic dissipativity analysis and control.