An asymptotic stability theorem of Peuteman–Aeyels for Itô processes and its applications in synchronous switching systems

2006 ◽  
Vol 55 (12) ◽  
pp. 963-970 ◽  
Author(s):  
Haijun Liu ◽  
Xiaowu Mu
Keyword(s):  
Asymptotic Stability ◽  
Stability Theorem ◽  
Switching Systems ◽  
Synchronous Switching

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 Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

2007 ◽  
Vol 49 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Zhenting Hou ◽  
Hailing Dong ◽  
Peng Shi
Keyword(s):  
Markov Chain ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Switching Systems ◽  
Switching System ◽  
Nonlinear Stochastic Systems ◽  
Semi Markov Process ◽  
Markovian Switching Systems ◽  
Semi Markov Processes

abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.

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.

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