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 multi-channel systems in the differential-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 inequality properties. In such a framework, we characterize the feedback Nash equilibria over an infinite-time horizon via a set of non-fragile stabilizing state-feedback solutions corresponding to the constrained dissipativity problems. Moreover, we show that the existence of a weak-optimal solution to the constrained dissipativity problem is a sufficient condition for the existence of a feedback Nash equilibrium, whereas the set of non-fragile stabilizing state-feedback solutions is fully described in terms of a set of dilated linear matrix inequalities.