On the Reliable Disturbance Decoupling Feedback Equilibrium for Generalized Multi-Channel Systems

This technical note considers the problem of reliable disturbance decoupling for a generalized multichannel system in a game-theoretic framework. Specifically, we link the problem of stabilization of the multi-channel system to certain properties of controlled invariant subspaces that are associated with the problem of disturbance decoupling, where the structure induced from this family of invariant subspaces is used for a game-theoretic interpretation of the problem. We provide a sufficient condition for the existence of a set of feedback equilibria that maintain the robust stability of the system under possible single-channel controller/agent failure as well as in the presence of unknown disturbances in the system.