L2-gain of systems with input delay and controller failure: zero-order hold model

This paper studies the stability and L₂-gain problem for a class of systems with input delay subject to controller failure. When the controller fails, zero-order hold is adopted. The paper addresses how long and how frequent the failure can be and still maintain the system exponentially stable and weighted L₂-gain. We first utilize switched delay systems including unstable subsystems to describe the controller failure problem. Then, the concepts of controller average failure frequency and failure length rate are introduced. Next, based on a novel piecewise Lyapunov functional including the largedelay-integral terms (LDIT), sufficient conditions guaranteeing exponential stability and weighted L₂-gain of the considered system are developed.