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The paper is concerned with the problem of input-to-state stability (ISS) for a class of systems with large delay period (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may include an unstable subsystem. Then based on a piecewise Lyapunov functional, the ISS conditions of the systems...
This paper studies the stability for a class of systems with time-varying delay subject to controller failure. It explores under what conditions of controller failure the system is still exponentially stable. The concept of controller failure frequency is introduced. First, the delay system with failed controller is modelled as a class of switched delay systems. Next, based on two lemmas developed...
In this paper, problems of stability and L2-gain for switched systems with time-varying delay and disturbance input are studied. Some subsystems can be unstable. By using an average dwell time approach incorporated with a piece-wise Lyapunov functional, sufficient conditions for exponential stability and weighted L2-gain of such systems, where not all subsystems are stable, are obtained in the form...
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