<p>The multiple generalized stability of nonlinear systems with impulsive disturbance and distributed delays is studied in this paper. By using the state space partition method, the number of multiple equilibrium points for <i>n</i>-dimensional system is given by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\prod _{i=1}^{n}(2K_i + 1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mo>∏</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with integer <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$K_i \ge 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>≥</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, and the sufficient conditions for generalized stability of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\prod _{i=1}^{n}(K_i + 1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mo>∏</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> equilibrium points are derived. Finally, the theoretical results are illustrated by using the simulations of an example.</p>

Multiple generalized stability of nonlinear delayed systems subject to impulsive disturbance

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发表日期：

2025年4月19日

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Fanghai Zhang,
Changlin Zhan

摘要

The multiple generalized stability of nonlinear systems with impulsive disturbance and distributed delays is studied in this paper. By using the state space partition method, the number of multiple equilibrium points for n-dimensional system is given by $\prod _{i=1}^{n}(2K_i + 1)$ $\prod_{i = 1}^{n} (2 K_{i} + 1)$ with integer $K_i \ge 0$ $K_{i} \geq 0$ , and the sufficient conditions for generalized stability of $\prod _{i=1}^{n}(K_i + 1)$ $\prod_{i = 1}^{n} (K_{i} + 1)$ equilibrium points are derived. Finally, the theoretical results are illustrated by using the simulations of an example.