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The notion of integral input-to-state stability (integral-ISS) is now recognized as a central concept in nonlinear systems analysis. In this work, we explore the Razumikhin approach to the integral-ISS property for systems with delays. The main idea is to treat the delayed state variable as a disturbance input. The results in this work extend the previous results on the Razumikhin method in the contexts...
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
In this paper, we study pattern preserving path following control of unicycle teams with communication delays. The pattern of the vehicle team is said to be preserved if the distance between it and the desired one remains in some given range. A virtual vehicle formation is introduced such that each virtual vehicle becomes the pursuit target for the corresponding real vehicle. First, an input-driven...
This paper presents further results on the problem of establishing stability of retarded nonlinear interconnected systems comprising integral input-to-state stable subsystems. It is shown that the stability of the interconnected systems with respect to external signals can be verified by constructing Lyapunov-Krasovskii functionals explicitly whenever small-gain type conditions are satisfied. The...
In this paper, interconnected retarded nonlinear systems are considered. Both the constant discrete and distributed time-delays in the subsystems and the interconnections are addressed. A sufficient small-gain type condition for integral input-to-state stability with respect to external inputs is provided in the framework of Lyapunov-Krasovskii functionals.
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