Characterization of robust feedback Nash equilibrium for multi-channel systems

In this paper, we consider the problem of robust state-feedback stabilization for multi-channel systems from a game-theoretic framework. In such a framework, we characterize the feedback Nash equilibria via a set of stabilizing state-feedback solutions corresponding to a family of perturbed multi-channel systems with dissipativity properties. Specifically, we show that the existence of a weak-optimal solution to a set of constrained dissipativity problems is a sufficient condition for the existence of a feedback Nash equilibrium, whereas the set of robust stabilizing state-feedback solutions is completely described in terms of a set of extended linear matrix inequalities.