Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities

We consider the problem of state-feedback stabilization for a multi-channel system in a game-theoretic framework, where the class of admissible strategies for the players is induced from a solution set of the individual objective functions that are associated with certain dissipativity properties of the system. In such a framework, we characterize the feedback Nash equilibria via a set of non-fragile stabilizing state-feedback solutions corresponding to a family of perturbed multi-channel systems. Moreover, 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 non-fragile stabilizing state-feedbacks solutions is described in terms of a set of dilated linear matrix inequalities.