Lyapunov-Razumikhin Function Research Articles

652 非線形時間遅れ最小位相系の安定条件(振動応用と制御, OS-10 非線形力学と力学系理論)

In this paper nonlinear minimum phase systems with time delay in state variables are considered. Time delay is an applied problem. It is well known that some examples are given in biology chemistry, economics, mechanics, physics, physiology, population dynamics, as well as in engineering sciences. Stability theory on the time delay system, generally expressed as functional differential equation, is useful to address those problems. However stability theory of functional differential equation is immature, and further development is expected. In the case of nonlinear functional differential equation, effective analysis tools are limited to Lyapunov-Krasovskii pan-function and Lyapunov-Razumikhin function. Objective in this paper is to propose one of the stability distinctions toward nonlinear functional differential equation.

Adaptive robust control based on Lyapunov-Razumikhin function for uncertain nonlinear time-delay systems

This paper investigates adaptive stabilization problem for nonlinear time-delay systems with parametric uncertainty. A LaSalle-Yoshizawa-like theorem established on LaSalle-Razumikhin invariant set theorem is given, which provides a sufficient condition for the convergence of the partial states with boundedness of the time-delay system. Using the proposed theorem, an adaptive stabilizing controller is derived for uncertain nonlinear time-delay systems. Moreover, it is also shown that the adaptive stabilization problem for the nonlinear time-delay system with strict parametric-feedback form can be solved by recursively constructing Lyapunov-Razumikhin function satisfying the proposed condition.

Delays-Dependent Stability for Linear Systems with Several Delays: An LMI Approach

This paper focuses on the problem of asymptotic stability of a class of time-delay systems described by linear delayed state equations involving several constant but unknown delays. A sufficient delays-dependent stability condition of the considered system is given using a Lyapunov-Razumikhin function approach. Furthermore, by transforming the stability problem into a linear matrix inequality optimization problem, the approach adopted here allows the computation of a suboptimal largest ellipsoidal stability region in the delays parameter space such that the asymptotic stability of the time-delay system is ensured.