Exponential Stability Analysis and Stabilization for Continuous Time-Delay Systems with Controller Failure

In this brief, we study the problem of controller synthesis for time-delay systems with controller failures based on an input-output approach. First, the time-delay system with controller failure is modeled as an input-output form. Next, the stability condition of the system with controller failure is developed via scaled small gain theorem. Additionally, the proposed stability condition is also testified by the direct Lyapunov functional method. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new model of the investigated system, a new triangle inequality and a new Lyapunov-Krasovskii functional. The proposed stability condition is demonstrated to be less conservative than other existing results. Moreover, the problem of stabilization is further solved with admissible controller designed via convex optimizations. The effectiveness of the proposed method is also illustrated via a numerical example.