$L_{2}$ -Gain of Systems With Input Delays and Controller Temporary Failure: Zero-Order Hold Model

This brief studies the stability and L₂-gain problem for a class of systems with input delays subject to the temporary failure of the controller. The input delay is interval time-varying. When the controller fails, the zero-order hold is adopted. An unstable system may occur due to the large interval delay bound caused by controller temporary failure. The brief addresses how long and how frequent the failure can be and still maintain the system exponentially stable and weighted L₂-gain. A novel piecewise Lyapunov functional, which includes the large-delay-integral terms, is applied. Under the restrictions of controller failure frequency and failure length rate, sufficient conditions guaranteeing exponential stability and weighted L₂-gain of the system are developed. Finally, the proposed criterion is applied to the networked control systems to show the effectiveness of the proposed method.