Decentralized HH-infinity control of complex systems with delayed feedback

The paper studies the problem of decentralized H∞H∞ fault tolerant state feedback control design for a class of continuous-time complex systems composed of identical subsystems and symmetric interconnections. We consider a time-varying interval-bounded delay in the feedback of each channel. Single delay as well as multiple delay cases is considered. By exploiting a particular structure of the systems, sufficient conditions are derived for the gain matrix selection. The controller design is performed using a reduced-order system under linear matrix inequality approach constraints. The asymptotic stability with disturbance attenuation γγ of the overall multiple delay closed-loop system is guaranteed when synthesizing the gain matrix into the decentralized controller. Moreover, sufficient conditions for the H∞H∞ bound tolerance under local control channel failures of the overall closed-loop system are derived. The tolerance can be easily tested on several low-order systems. A numerical example illustrates the effectiveness of the proposed method.