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Input-to-state Stability Analysis of a Class of Nonlinear Impulsive System

Author: PengChunXiao
Tutor: HuJunHao
School: Central South University for Nationalities
Course: Applied Mathematics
Keywords: Nonlinear System Impulsive System Stability Input-to-stateStability Integral Input-to-state Stability
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 16
Quote: 0
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In the classical control theory, the stability problem is one of the most basic andimportant problems when studying all kinds of dynamic systems. In the modern controltheory, it is still an important research direction.Because the linear system satisfies superposition principle, the conclusion ofstability analysis when moving freely is consistent with the conclusion of stabilityanalysis when having external excitation, But the nonlinear system is not satisfied theconclusion.For stability analysis of nonlinear systems, there are many different types ofstability problems. For example, Lyapunov stability-without any external signalexcitation, the state of the system can be back to itself inherent stability properties ofequilibrium state from any initial point, therefore it calls the Lyapunov stability of theequilibrium point. Input-to-state stability(ISS)-under bounded external signalexcitation, the state of the system response to stay within the scope of the boundedstability.Because the nonlinear system may have finite escape time and escape phenomenon,even the system is stable at the equilibrium point when moving freely, but a smallexternal excitation may also make the system state and the output response becomedivergent instability. So for nonlinear system, its two kinds of stability must bediscussed respectively.This paper mainly studies the input-to-state stability and integral input-to-statestability of a class of nonlinear impulsive system. And under certain conditions,sufficient conditions are given which guarantee input-to-state stability and integralinput-to-state stability for the system respectively.First of all in the introduction section, we introduced the research background,significance of research, and the status of the study in and abroad of impulsive system,so we formed a preliminary understanding of the content of the research. In the second chapter, we elaborated some basic definitions, relational prepareknowledge, and the meaning of symbols in this paper, to prepare for the next research.In the third chapter, under certain conditions, one corollary and two sufficientconditions are established which guarantee input-to-state stability for nonlinearimpulsive system in this paper.Finally in the fourth chapter, under certain conditions, one sufficient condition andtwo corollaries are established further which guarantee input-to-state stability fornonlinear impulsive system in this paper.

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