scholarly journals Integral Stability in Terms of Two Measures for Nonlinear Differential Systems with “Maxima”

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguang Wang ◽  
Qing Xu ◽  
Xiaojing Liu
Keyword(s):  
Comparison Principle ◽  
Lyapunov Functions ◽  
Differential Systems ◽  
Two Measures ◽  
Integral Stability ◽  
Nonlinear Differential Systems

This paper investigates relatively integral stability in terms of two measures for two differential systems with “maxima” by employing Lyapunov functions, Razumikhin method, and comparison principle. An example is given to illustrate our result.

scholarly journals The Stability of Nonlinear Differential Systems with Random Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Miroslava Růžičková
Keyword(s):  
Trivial Solution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
New Method ◽  
Random Parameters ◽  
Differential Systems ◽  
The Stability ◽  
Nonlinear Differential Systems

The paper deals with nonlinear differential systems with random parameters in a general form. A new method for construction of the Lyapunov functions is proposed and is used to obtain sufficient conditions forL2-stability of the trivial solution of the considered systems.

scholarly journals Practical Stability and Integral Stability for Singular Differential Systems with Maxima

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Junyan Bao ◽  
Peiguang Wang ◽  
Yanjun Li
Keyword(s):  
Comparison Principle ◽  
Lyapunov Method ◽  
Practical Stability ◽  
Differential Systems ◽  
Integral Stability

In this paper, we introduce various definitions of practical stability and integral stability for nonlinear singular differential systems with maxima and give criteria of stability for such systems via the Lyapunov method and comparison principle.

scholarly journals Stability of nonlinear systems under constantly acting perturbations

1995 ◽  
Vol 18 (2) ◽  
pp. 273-278 ◽  
Author(s):  
Xinzhi Liu ◽  
S. Sivasundaram
Keyword(s):  
Nonlinear Systems ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Differential Systems ◽  
Lyapunov’S Direct Method ◽  
Two Measures ◽  
Total Stability ◽  
Nonlinear Differential Systems

In this paper, we investigate total stability, attractivity and uniform stability in terms of two measures of nonlinear differential systems under constant perturbations. Some sufficient conditions are obtained using Lyapunov's direct method. An example is also worked out.

scholarly journals Existence of periodic solutions of impulsive differential systems

1991 ◽  
Vol 4 (2) ◽  
pp. 137-146 ◽  
Author(s):  
L. H. Erbe ◽  
Xinzhi Liu
Keyword(s):  
Periodic Solutions ◽  
Comparison Principle ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Existence Of Periodic Solutions ◽  
Piecewise Continuous

In this paper, the existence of periodic solutions of impulsive differential systems is considered. Since the solutions of such a system are peicewise continuous, it is necessary to introduce piecewise continuous Lyapunov functions. By means of such functions, together with the comparison principle, some sufficient conditions for the existence of periodic solutions of impulsive differential systems are established.

Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

2018 ◽  
Vol 15 (1) ◽  
pp. 84-93
Author(s):  
V. I. Volovach ◽  
V. M. Artyushenko
Keyword(s):  
Spectral Characteristics ◽  
Random Processes ◽  
Spectral Densities ◽  
Differential Systems ◽  
Non Gaussian ◽  
Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

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