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Stability Analysis of Impulsive Switched Systems

Author: YuWenLei
Tutor: FuXiLin
School: Shandong Normal University
Course: Applied Mathematics
Keywords: The pulse differential switch system Lyapunov function Two Measures (h0, h) - stability Strictly stable Exponentially stable
CLC: TP13
Type: Master's thesis
Year: 2010
Downloads: 58
Quote: 1
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Abstract


In this paper, considering impulsive differential switching system which fk-1 ∈ C (R × Rn, Rn), Ik ∈ C (R x Rn, Rn), 0 lt; t0 lt; t1 lt; ... lt; tk lt; ... ( ?) tk = ∞. stability analysis of the system in switching time into pulse skipping pulse the differential switching system stability results and give appropriate examples to illustrate the application of the theorem. switching system as an important hybrid dynamic systems, usually by continuous dynamic subsystem combined switch mapping constituted, is widely used in many emerging areas such as neural networks, secure communication, intelligent control, power systems, aerospace, in recent years, switching system increasingly hot research made many research results, the stability of the switching system. addition, the pulse phenomenon is an instantaneous jump phenomenon prevalent in the practical problems in the field of science and technology, in practice, with a pulse systems are often more accurate description of the objective laws of this state moment jump. recent years, the the impulsive differential switching system has attracted more and more attention from scholars and research, but impulsive differential to switching system stability results is still relatively small. system of this study is the first study in the literature, but only the exponential stability of the research system. Given the practical significance and theoretical value, the paper studies impulsive differential switch terms of two measures of stability, the strict solution the index of the stability of the zero solution is stable, specific content is divided into three chapters. Chapter III, we first use of a system of ordinary differential comparison theorem, scalar impulsive differential switching system to compare system using Lyapunov function differential inequality impulsive differential switching system comparison theorem applied to stability studies, and then in the first chapter of the fourth quarter will its impulsive differential switching system on the stability of the result of the comparison of the two measure should be pointed out Using comparison theorem inference, we can compare the system be extended to impulsive differential systems, stability of impulsive differential systems the pulse switching system stability, the results are applied more widely and we can get the system about two measure direct result of the stability at the same time, gives examples are given to illustrate the effectiveness of the theorem we know, Lyapunov stability of the trivial solution of a differential system and can not be ruled out asymptotically stable may, and, if the trivial solution is asymptotically stable just nonzero solution is sufficiently close to the trivial solution tends to zero, and can not characterize the rate of decay of these solutions in other words, Lyapunov stability the concept only solution unilateral estimated, are not strictly strict stability of the research system, give a lower bound estimate of the solution is very important. differential system the strict stability studies are rare. Chapter II Lyapunov direct method and comparison principle of pulse differential switch strict zero solution stability of the system, by constructing two different nature Lyapunov function to study, some sufficient conditions to determine the strict stability of impulsive differential switch system, since it is composed by the different systems, so constructed to meet the conditions of the common Lyapunov function will encounter some difficulties In the third chapter, using multiple Lyapunov function method to study the stability of the pulse the differential switching system zero solution index for impulsive differential switch system subsystem construct different Lyapunov function Lyapunov function has a certain relationship, and with the switching time between the length of the linked judgment impulsive differential switching system Some sufficient conditions of exponential stability, and based on the theorem and

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