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Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Input-to-State Stability of Large-Scale Stochastic Impulsive Systems with Time Delay and Application to Control Systems

Authors : M. S. Alwan, X. Z. Liu, W.-C. Xie

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

This chapter deals with large-scale nonlinear delay stochastic systems where the system states are subject to impulsive effects and perturbed by some disturbance input having bounded energy. The interest is to develop a comparison principle and establish input-to-state stability (ISS) in the mean square (m.s.) using vector Lyapunov function and Razumikhin technique. Impulses are being viewed as perturbation to stable systems, and they have a stabilizing role to unstable systems.

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previous chapter Solving the Linear Transportation Problem by Modified Vogel Method
next chapter Replicator Dynamics of Axelrod’s Norms Games
Literature
1.
Alwan, M.S., Liu, X.Z., Xie, W-C.: Existence, continuation, and uniqueness problems of stochastic impulsive systems with time delay. J. Frankl. Inst. 347 , 1317–1333 (2010)
2.
Alwan, M.S.: Qualitative properties of stochastic hybrid systems and applications. Ph. D. Thesis, University of Waterloo, Ontario, Canada (2011)
3.
Hespanha, J.P., Liberzon, D., Tell, A.R.: On input-to-state stability of impulsive systems. Proceeding of the 44th Conference on Decision and Control, and the European Control Conference, Seville, Spain, 12–15 December (2005)
4.
Lakshmiknatham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)CrossRef
5.
Michel, A.N., Miller, R.K.: Qualitative Analysis of Large Scale Dynamical Systems. Academic, New York (1977)MATH
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7.
Teel, A.R, Moreau, L, Nesic, D.: A unified framework for input-to-state stability in systems with two time scales. IEEE Trans. Automat. Control 48(9), 1526–1544 (2003)MathSciNetCrossRef
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Zecevic, A., Silijak, D.D.: Control of Complex Systems: Structural Constraints and Uncertainty. Springer, New York (2010)
Metadata
Title
Input-to-State Stability of Large-Scale Stochastic Impulsive Systems with Time Delay and Application to Control Systems
Authors
M. S. Alwan
X. Z. Liu
W.-C. Xie
Copyright Year
2015
Book
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Print ISBN: 978-3-319-12306-6

Electronic ISBN: 978-3-319-12307-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12307-3_4

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