Augmented Lyapunov functional for the calculation of stability interval for time-varying delay

2007 ◽  
Vol 1 (1) ◽  
pp. 381-386 ◽  
Author(s):  
Y. He ◽  
G.P. Liu ◽  
D. Rees
Keyword(s):  
Lyapunov Functional ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

STABILITY CRITERION OF A CLASS OF NEUTRAL NEURAL NETWORK WITH UNCERTAINTIES AND TIME-VARYING DELAY

2011 ◽  
Vol 08 (01) ◽  
pp. 75-82
Author(s):  
JIANJUN TU ◽  
HANLIN HE
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Lyapunov Equation ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
Uniformly Asymptotic Stability ◽  
The Stability ◽  
Varying Delay

Under reasonable postulated conditions of time-varying delay, the stability of a class of neutral neural network is probed. Based on the proper construction of the Lyapunov functional, a new method of predicating the uniformly asymptotic stability of this kind of neutral network is presented. The criterion is based on the positive definite solutions of a Riccati equation and a discrete Lyapunov equation, and is converted to LMI problem. The validity of the criterion is also confirmed by the simulation.

scholarly journals A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganji Huang ◽  
Shixian Luo ◽  
Linna Wei ◽  
Wuhua Chen
Keyword(s):  
Switched Systems ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
System Parameters ◽  
Time Varying Delay ◽  
Lyapunov Functional Method ◽  
The Stability ◽  
Varying Delay

This paper deals with the stability of switched systems with time-varying delay. The time-varying system parameters are assumed to be norm-bounded. Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Finally, the proposed method is applied to a numerical example and the simulative results are also given.

scholarly journals A Lyapunov functional for a system with a time-varying delay

2012 ◽  
Vol 22 (2) ◽  
pp. 327-337 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Lyapunov Functional ◽  
Linear Time ◽  
Time Derivative ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Time Varying Delay ◽  
Analytical Formulas ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Varying Delay

A Lyapunov functional for a system with a time-varying delay The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

Adaptive-observer-based robust control for a time-delayed teleoperation system with scaled four-channel architecture

Robotica ◽  
2021 ◽  
pp. 1-21
Author(s):  
Linping Chan ◽  
Qingqing Huang ◽  
Ping Wang
Keyword(s):  
Lyapunov Functional ◽  
Adaptive Observer ◽  
System Stability ◽  
Time Varying ◽  
Model Uncertainties ◽  
Control Approach ◽  
Time Varying Delay ◽  
Teleoperation System ◽  
Teleoperation Systems ◽  
Varying Delay

Abstract This article presents an innovative adaptive-observer-based scaled four-channel (4-CH) control approach applying damping injection for nonlinear teleoperation systems, which unify the study of robotic dynamic uncertainties, operator/environment force acquirements and asymmetric time-varying delays in the same framework. First, a scaled 4-CH scheme with damping injection is developed to handle time-varying delay while guaranteeing the passivity of communication channels. Then, the improved extended active observer (IEAOB) is deployed to derive the operator/environment force while addressing the issues of measurement noise and model uncertainties. Furthermore, the system stability is analyzed by choosing Lyapunov functional. Finally, the proposed method is validated through simulation.

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