Abstract:

The problem of resilient static output feedback stabilization was investigated for controlled positive timedelay systems with interval uncertainties. By introducing a small scalar, a necessary and sufficient condition was obtained for the asymptotical stability of positive timedelay systems, which was more useful when designing output feedback controllers since the Lyapunov matrix was separated from the system matrices. Based on the above condition and by utilizing the technique of matrix inequality, for different cases of the control matrix, necessary and sufficient／sufficient conditions were established for the existence of the resilient controller with interval additive gain variation and  detailed expressions of the controller were also given. The desired controller gain matrices could be effectively determined  via  cone complementarity linearization techniques. A numerical example was presented to illustrate the effectiveness of the proposed method.

Key words:  positive systems, delayed systems, output feedback stabilization, resilient control, cone complementarity linearization