Decentralized stabilization of complex systems with delayed feedback

Abstract

The paper studies the problem of decentralized state feedback control design for a class of continuous-time complex systems. These systems are composed of identical nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations. We consider local time-varying delayed feedback at each channel. Single delay as well as multiple delay cases are considered. By exploiting the special structure of the systems, sufficient conditions are derived for the gain matrix selection performed on the design system of reduced dimension under linear matrix inequality approach constraints. It is shown that the robust delay-dependent stability of the global multiple delay closed-loop system is guaranteed when implementing the gain matrix into the global decentralized controller. Moreover, sufficient conditions are derived for the tolerance of local control channel failures in such a global closed-loop system. The fault tolerance can be effectively tested on systems of reduced dimensions.