scholarly journals A novel approach to exponential stability of nonlinear systems with time-varying delays

2011 ◽  
Vol 235 (6) ◽  
pp. 1700-1705 ◽  
Author(s):  
Song Xueli ◽  
Peng Jigen
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Time Varying ◽  
Novel Approach

scholarly journals Exponential Stability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays via an Average Dwell-Time Method

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
N. Yotha ◽  
T. Botmart ◽  
T. Mouktonglang
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Fast Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Unstable Subsystems

The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.

New criteria for global exponential stability of linear time-varying volterra difference equations

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Trung Hieu Le
Keyword(s):  
Exponential Stability ◽  
Difference Equations ◽  
Global Exponential Stability ◽  
Linear Time ◽  
Time Varying ◽  
Novel Approach ◽  
New Criteria ◽  
Volterra Difference Equations ◽  
Explicit Criteria

AbstractLinear time-varying Volterra difference equations are considered. By a novel approach, we get some new explicit criteria for global exponential stability. Some examples are given to illustrate the obtained results. To the best of our knowledge, the obtained results are new.

EXPONENTIAL STABILITY OF A CLASS OF POSITIVE NONLINEAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

2020 ◽  
Vol 65 (6) ◽  
pp. 3-12
Author(s):  
Dung Le Thi Hong
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Time Varying ◽  
System State ◽  
Numerical Example ◽  
Comparison Technique

This paper is concerned with the problem of exponential stability of a class of positive nonlinear systems with heterogeneous time-varying delays which describe a model of Hopfield neural networks with nonlinear self-inhibition rates. Based on a novel comparison technique via a differential and integral inequalities, testable conditions are derived to ensure system state trajectories converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.

Exponential Stability of Slowly Time-Varying Nonlinear Systems

2002 ◽  
Vol 15 (3) ◽  
pp. 202-228 ◽  
Author(s):  
Joan Peuteman ◽  
Joan Peuteman ◽  
Dirk Aeyels
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Time Varying

On stability of nonlinear neutral functional differential equations

2017 ◽  
Vol 24 (1) ◽  
pp. 89-104 ◽  
Author(s):  
Pham Huu Anh Ngoc ◽  
Thai Bao Tran ◽  
Cao Thanh Tinh
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Challenging Problem ◽  
Neutral Functional Differential Equations ◽  
Novel Approach ◽  
Functional Differential

We address the challenging problem of the exponential stability of nonlinear time-varying functional differential equations of neutral type. By a novel approach, we present explicit sufficient conditions for the exponential stability of nonlinear time-varying neutral functional differential equations. A discussion of the obtained results and illustrative examples are given.

scholarly journals Exponential Stability of Switched Positive Homogeneous Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Dadong Tian ◽  
Shutang Liu
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Decay Rate ◽  
Dwell Time ◽  
Vector Fields ◽  
Sufficient Condition ◽  
Time Varying ◽  
Time Switching ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector

This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-varying delays is derived. In particular, for the corresponding delay-free systems, we prove that this sufficient condition is also necessary. Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

Sign in / Sign up

Export Citation Format

Share Document