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The Research of Stablility of Nonlinear Impulsive Differential Systems

Author: HaoZhenFu
Tutor: OuYangZiGen
School: Nanhua University
Course: Applied Mathematics
Keywords: Impulsive differentialsystem Lyapunov function stability M-matrix Convergent rate
CLC: O175.13
Type: Master's thesis
Year: 2011
Downloads: 36
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Abstract


The research of impulsive differential systems begins in the 1960s. A lot of research materials have shown that impulsive differential systems which have vital theoretical significance and practical value, have been involved in many fields, such as information sciences, control systems, life sciences and so on. In this dissertation, we study some stability properties for a impulsive differential systems employing Lyapunov’s second method. Herein these stability results do not require a Lyapunov function to have a negative definite first derivative along trajectories of the system, further we may not require its derivative to restrict the function increasing growth; and we do not give conditions on continuous portion or discrete portion of the systems respectively, hence we can give mixing conditions on them. Base on this idea, we give a series of sufficient conditions to determine stability properties of impulsive differential systems. Using the properties of differential inequality and M-matrix, sufficient conditions for the solutions of exponential asymptotic stability of nonlinear neutral differential systems with impulsive delay are studied in this paper.The dissertation includes four chapters, which is summarized as follows.In ChapterⅠ, the wide applications of impulsive differential systems are introduced,which shows the theoretical significance and practical value of the research. The development of impulsive theory is introduced, so are the development of stability theory and its research outline.ChapterⅡ, as preliminaries, introduces some fundamental concepts of impulsive differential systems and some related results to the stability of solutions of impulsive differential systems. ChapterⅢ, we study some stability properties for a impulsive differential systems employing Lyapunov’s second method. we give a series of sufficient conditions to determine stability properties of impulsive differential systems.In ChapterⅣ, using the properties of differential inequality and M-matrix, sufficient conditions for the solutions of exponential asymptotic stability of nonlinear neutral differential systems with impulsive delay are studied in this paper.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations > Stability theory
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