Nash Equilibrium Seeking with Linear Time-Invariant Dynamic Agents

Game with linear time-invariant dynamic agents is explored for the case where the payoff function of each agent is concave and continuously differentiable. By using passivation, a control law that asymptotically stabilize the Nash equilibrium is proposed. We use passivation to derive our control laws. We illustrate our approach with a numerical example. We also characterized the class of linear time-invariant system that can be made passive with respect to its output by dynamic feedback.