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<p>This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear time-varying systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution. Secondly, we propose new finite-time stability and instability criteria that relax the constraints on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{L}V\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">L</mi> </mrow> <mi>V</mi> </math></EquationSource> </InlineEquation> (the infinitesimal operator of Lyapunov function <i>V</i>) by the uniformly asymptotically stable function. On the one hand, these obtained results make up for the shortcomings of the existing results. On the other hand, the new finite-time stability theorems can be viewed as natural extensions of the existing results and also allow <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{L}V\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">L</mi> </mrow> <mi>V</mi> </math></EquationSource> </InlineEquation> to be indefinite (negative or positive) rather than just only allow <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{L}V &lt; 0\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">L</mi> </mrow> <mi>V</mi> <mo>&lt;</mo> <mn>0</mn> </math></EquationSource> </InlineEquation>. Finally, some simulation examples verify the validity of the theoretical results.</p>

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New results on finite-time stability and instability theorems for stochastic nonlinear time-varying systems

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Weihai Zhang,
  • Liqiang Yao

摘要

This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear time-varying systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution. Secondly, we propose new finite-time stability and instability criteria that relax the constraints on \(\mathcal{L}V\) L V (the infinitesimal operator of Lyapunov function V) by the uniformly asymptotically stable function. On the one hand, these obtained results make up for the shortcomings of the existing results. On the other hand, the new finite-time stability theorems can be viewed as natural extensions of the existing results and also allow \(\mathcal{L}V\) L V to be indefinite (negative or positive) rather than just only allow \(\mathcal{L}V < 0\) L V < 0 . Finally, some simulation examples verify the validity of the theoretical results.