Stability, asymptotic and exponential stability for various types of equations with discontinuous solutions via Lyapunov functionals

2021 ◽  
Vol 299 ◽  
pp. 256-283
Author(s):  
Claudio A. Gallegos ◽  
Rogelio Grau ◽  
Jaqueline G. Mesquita
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functionals ◽  
Discontinuous Solutions

scholarly journals Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

2012 ◽  
Vol 17 (2) ◽  
pp. 210-222 ◽  
Author(s):  
Xiu Liu ◽  
Shouming Zhong ◽  
Xiuyong Ding
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Functionals ◽  
Sufficient Condition ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Numerical Example ◽  
Impulsive Switched Systems ◽  
Theoretical Results

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

scholarly journals Dynamic Analysis of Nonlinear Impulsive Neutral Nonautonomous Differential Equations with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jinxian Li
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Exponential Stability ◽  
Dynamic Analysis ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Lyapunov Functionals ◽  
Nonautonomous Differential Equations ◽  
Inequality Technique

A class of neural networks described by nonlinear impulsive neutral nonautonomous differential equations with delays is considered. By means of Lyapunov functionals and differential inequality technique, criteria on global exponential stability of this model are derived. Many adjustable parameters are introduced in criteria to provide flexibility for the design and analysis of the system. The results of this paper are new and they supplement previously known results. An example is given to illustrate the results.

scholarly journals Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Youssef Raffoul ◽  
Habib Rai
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Infinite Delay ◽  
Zero Solution ◽  
Uniform Stability ◽  
Lyapunov Functionals ◽  
Integro Differential Equation ◽  
The Stability

AbstractIn [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation

scholarly journals Stability of Nonlinear Stochastic Discrete-Time Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yan Li ◽  
Weihai Zhang ◽  
Xikui Liu
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Lyapunov Functionals ◽  
Discrete Time Systems ◽  
The Stability ◽  
Efficient Criteria ◽  
Time Systems ◽  
Moment Exponential Stability ◽  
Theoretical Results

This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, andpth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.

NOVEL EXPONENTIAL STABILITY CONDITIONS FOR A CLASS OF INTERVAL PROJECTION NEURAL NETWORKS

2009 ◽  
Vol 02 (03) ◽  
pp. 287-297 ◽  
Author(s):  
ZIXIN LIU ◽  
SHU LÜ ◽  
SHOUMING ZHONG
Keyword(s):  
Neural Networks ◽  
Quadratic Programming ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Convex Quadratic Programming ◽  
Stability Conditions ◽  
Lyapunov Functionals ◽  
Numerical Example ◽  
Grönwall Inequality ◽  
Quadratic Programming Problems

In this paper, a class of interval projection neural networks for solving quadratic programming problems are investigated. By using Gronwall inequality and constructing appropriate Lyapunov functionals, several novel conditions are derived to guarantee the exponential stability of the equilibrium point. Compared with previous results, the conclusions obtained here are suitable not only to convex quadratic programming problems but also to degenerate quadratic programming problems, and the conditions are more weaker than the earlier results reported in the literature. In addition, one numerical example is discussed to illustrate the validity of the main results.

GLOBAL EXPONENTIAL STABILITY CONDITIONS FOR DELAYED PARABOLIC NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 17 (12) ◽  
pp. 4409-4415
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Lyapunov Functionals ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients.

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