scholarly journals On a partial asymptotic stability theorem of Willett and Wong

1978 ◽  
Vol 63 (2) ◽  
pp. 416-420 ◽  
Author(s):  
Frederick J. Scott
Keyword(s):  
Asymptotic Stability ◽  
Stability Theorem

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Najah F. Jasim
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
External Disturbances ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Arbitrary Switching

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

scholarly journals Stability in mixed linear delay Levin-Nohel integro-dynamic equations on time scales

2019 ◽  
Vol 38 (5) ◽  
pp. 73-86
Author(s):  
Kamel Ali Khelil ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Asymptotic Stability ◽  
Contraction Mapping ◽  
Zero Solution ◽  
Stability Theorem ◽  
Necessary And Sufficient Condition ◽  
Contraction Mapping Theorem ◽  
Linear Delay ◽  
Several Delays ◽  
Necessary And Sufficient ◽  
Stability Results

In this paper we use the contraction mapping theorem to obtain asymptotic stability results about the zero solution for the following mixed linear delay Levin-Nohel integro-dynamic equation    x^{Δ}(t)+∫_{t-r(t)}^{t}a(t,s)x(s)Δs+b(t)x(t-h(t))=0, t∈[t₀,∞)∩T,where f^{△} is the △-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung <cite>d</cite>. In addition, the case of the equation with several delays is studied.

scholarly journals Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Junyan Bao ◽  
Peiguang Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Stability Theorem ◽  
Point Method ◽  
Functional Differential ◽  
Necessary And Sufficient

This paper studies a class of nonlinear neutral set-valued functional differential equations. The globally asymptotic stability theorem with necessary and sufficient conditions is obtained via the fixed point method. Meanwhile, we give an example to illustrate the obtained result.

scholarly journals Stability and asymptotic stability in impulsive semidynamical systems

1994 ◽  
Vol 7 (4) ◽  
pp. 509-523 ◽  
Author(s):  
Saroop K. Kaul
Keyword(s):  
Asymptotic Stability ◽  
Stability Theorem ◽  
Invariance Theorem

In this paper we generalize two results of Lasalle's, the invariance theorem and asymptotic stability theorem of discrete and continuous semidynamical systems, to impulsive semidynamical systems.

scholarly journals The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

2021 ◽  
Vol 7 (3) ◽  
pp. 4795-4802
Author(s):  
Narongrit Kaewbanjak ◽  
◽  
Watcharin Chartbupapan ◽  
Kamsing Nonlaopon ◽  
Kanit Mukdasai ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Uniform Asymptotic Stability ◽  
Razumikhin Theorem ◽  
System With Delay ◽  
Fractional System ◽  
Delay Dependent

<abstract><p>This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.</p></abstract>

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