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首页> 外文期刊>Systems and Control Letters >Stability analysis of linear time-varying time-delay systems by non-quadratic Lyapunov functions with indefinite derivatives
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Stability analysis of linear time-varying time-delay systems by non-quadratic Lyapunov functions with indefinite derivatives

机译：具有无限衍生物的非二次Lyapunov功能线性时变时间延迟系统的稳定性分析

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This paper presents a stability analysis of linear time-varying (LTV) time-delay systems by using non quadratic Lyapunov functions and functionals. Two types of sufficient conditions are proposed for testing several different kinds of stability, such as asymptotic stability, exponential stability and uniformly exponential stability, for LTV systems without delay. Then, by constructing suitable non-quadratic Lyapunov functions (functionals) that are respectively the time-varying weighted L-1 and L-infinity norms of the state variables and by using properties of the uniformly asymptotically stable (UAS) function and the recently established improved Razumikhin and Krasovskii stability theorems, both delay- dependent and delay-independent conditions are proposed for testing uniformly exponential stability of a class of LTV time-delay systems. The time derivatives of the non-quadratic Lyapunov functions (functionals) along the solutions are allowed to be indefinite, namely, to take both negative and positive values. Numerical examples show that the non-quadratic Lyapunov functions (functionals) based methods are more efficient than the existing ones that are based on quadratic functions (functionals). (C) 2018 Elsevier B.V. All rights reserved.
机译：本文通过使用非二次Lyapunov函数和功能来介绍线性时变（LTV）时延系统的稳定性分析。提出了两种类型的充分条件，用于测试几种不同类型的稳定性，例如渐近稳定性，指数稳定性和均匀指数稳定性，用于LTV系统而没有延迟。然后，通过构造分别是状态变量的时变的加权L-1和L-Infinity标准的合适的非二次Lyapunov函数（功能），并且通过使用均匀渐近稳定（UAS）功能的特性和最近建立的提出了改进的Razumikhin和Krasovskii稳定性定理，包括延迟和延迟无关的条件，用于测试一类LTV时滞系统的均匀指数稳定性。允许沿溶液的非二次Lyapunov函数（功能）的时间衍生物被允许是无限期的，即取代负值和正值。数值示例表明，基于非二次Lyapunov函数（功能）的方法比基于二次函数（功能）的现有方法更有效。 （c）2018 Elsevier B.v.保留所有权利。

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