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ABSTRACT: The p-th moment exponential stability of stochastic differential equations with impulse effect is addressed. By employing the method
of vector Lyapunov functions, some sufficient conditions for the p-th moment exponential stability are established. In addition, the usual restriction of the growth rate of Lyapunov function
is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential stability. Several examples are also discussed to illustrate the effectiremess of the results obtained.
Keywordsstochastic differential equations–impulse–
p-th moment exponential stability–vector Lyapunov functions
Sciece China. Information Sciences 04/2012; 54(8):1702-1711. · 0.39 Impact Factor
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ABSTRACT: This article addresses the issue of designing an H ∞ output feedback controller for linear discrete-time systems with impulses. First, a new concept of H ∞ output feedback stabilisation for general linear discrete-time systems with impulses is introduced. Then sufficient linear matrix inequality conditions for the stabilisation and H ∞ performance of general discrete systems with impulses are proposed. In addition, the result is applied to resolve typical output feedback control problems for systems with impulses, such as the decentralised H ∞ output feedback control and the simultaneous H ∞ output feedback control. Finally, a numerical simulation is also presented to illustrate the effectiveness of the proposed results.
International Journal of Systems Science. 10/2010; 41(10):1221-1229.
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Stochastics and Dynamics - STOCH DYN. 01/2010; 10(03).
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ABSTRACT: This paper is concerned with the controllability and observability for linear time-varying switched impulsive systems. First, some new results about the variation of parameters for time-varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time-varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.
International Journal of Robust and Nonlinear Control 08/2009; 20(12):1313 - 1325. · 1.55 Impact Factor
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ABSTRACT: In this paper, we discuss the problem of H∞ filtering for a class of stochastic Markovian jump systems with impulsive effects. The aim is to design a stochastically stable filter, using the locally sampled measurements, which guarantee both the stochastic stability and a prescribed level of H∞ performance for the filtering error dynamics. A sufficient condition for the existence of such a filter is given in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is obtained. A numerical example is provided to show the effectiveness of the proposed results. Copyright © 2007 John Wiley & Sons, Ltd.
International Journal of Robust and Nonlinear Control 04/2007; 18(1):1 - 13. · 1.55 Impact Factor
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I. J. Bifurcation and Chaos. 01/2006; 16:3109-3112.
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ABSTRACT: In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.
Neurocomputing.
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ABSTRACT: In this paper we introduce a new stability—eventual practical stability for impulsive differential equations with time delay. By using Lyapunov functions and comparison principle, we will get some criteria of eventual practical stability, eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements.
Journal of Computational and Applied Mathematics.
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ABSTRACT: This paper introduces some new concepts of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching. Some stability criteria of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching are obtained by using Liapunov function method. An example is also discussed to illustrate the efficiency of the obtained results.
Automatica.
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ABSTRACT: This paper discusses nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. The lower and upper solutions and monotone iterative techniques are used to achieve the existence results. Two examples are provided to illustrate the efficiency of the obtained results.
Journal of Mathematical Analysis and Applications.
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ABSTRACT: This paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. An example is discussed to illustrate the efficiency of the obtained result.
Journal of Mathematical Analysis and Applications.
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ABSTRACT: In this paper, we derive some less stringent conditions for the exponential and asymptotic stability of impulsive control systems with impulses at fixed times. These conditions are then used to design an impulsive control law for Lü system, which drives the chaotic state to a zero equilibrium.
Chaos, Solitons & Fractals.
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ABSTRACT: We establish the oscillation criteria for the second order functional equationandNew oscillation criteria improve the one recently established by Manojlovic et al. [J. Manojlovic, Y. Shoukaku, T. Tanigawa, N. Yoshida, Oscillation criteria for second order differential equations with positive and negative coefficients, Appl. Math. Comp. 181 (2006) 853–863].
Applied Mathematics and Computation.
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ABSTRACT: In this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied. By using Lyapunov functions and Razumikhin techniques, some criteria of stability, asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided. Some examples are also presented to illustrate the efficiency of the results obtained.
Nonlinear Analysis: Theory, Methods & Applications.
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ABSTRACT: Based on the Lyapunov stabilization theory and matrix measure, this paper proposes some simple generic criterions of global chaos synchronization between two coupled time-varying chaotic systems from a unidirectional linear error feedback coupling approach. These simple criterions are applicable to some typical chaotic systems with different types of nonlinearity, such as the original Chua’s circuit and the Rössler chaotic system. The coupling parameters are determined according to the new criterion so as to ensure the coupled systems’ global chaos synchronization.
Chaos, Solitons & Fractals.
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ABSTRACT: In this Letter, several new theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the Rössler systems can be asymptotically controlled to the equilibrium point by using impulsive control. Given the parameters of the Rössler system and the impulsive control law. We also present a theory of impulsive synchronization of two Rössler systems. Moreover, a larger upper bound of impulsive intervals for the stabilization and synchronization can be obtained.
Physics Letters A. 306:306-312.
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ABSTRACT: In this paper, we address the problem of hybrid control for a class of stochastic non-linear Markovian switching systems. First, a hybrid controller is introduced for the systems. Then under some appropriate assumptions, the stabilization condition for the systems under pure impulsive control is given. Further under impulsive control, the output feedback stabilization problem of the systems is discussed and linear output feedback controllers are designed. Finally a numerical example is provided to illustrate the effectiveness of the proposed methods.
Automatica.
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ABSTRACT: In this Letter, the concept of impulsive robust control for uncertain Luré system and an impulsive robust control scheme of the uncertain Luré system are presented. We give some sufficient conditions for the stabilization and synchronization of uncertain Luré systems via impulsive control with varying impulsive intervals. The result is illustrated to be efficient through an example.
Physics Letters A.
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ABSTRACT: This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefer’s fixed point theorem. A numerical example is provided to show the effectiveness of the proposed results.
Automatica.
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ABSTRACT: This paper considers the problem of impulsive robust fault-tolerant feedback control for chaotic Lur’e systems. The sufficient condition of the uncertain Lur’e systems possessing integrity against actuator failures is given by using linear matrix inequalities (LMIs), and at the same time, the closed-loop system with impulsive effects is globally asymptotically stable, and it has robustness of parameter uncertainties. An example is given to illustrate obtained result.
Chaos, Solitons & Fractals.
