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2005•The ANZIAM JournalOpen access

A comparison principle and stability for large-scale impulsive delay differential systems

Xinzhi Liu, Xuemin Shen, Yi Zhang

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Abstract

Abstract This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

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Abstract This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

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Available abstract

Abstract This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

Key concepts: Nonlinear system, Stability (learning theory), Differential (mechanical device), Scale (ratio), Control theory (sociology), Delay differential equation, Mathematics, Differential equation

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