Stability in Impulsive Systems with Markov Perturbations in Averaging Scheme. I. Averaging Principle for Impulsive (original) (raw)
Related papers
Periodic averaging method for impulsive stochastic differential equations with Lévy noise
Applied Mathematics Letters, 2019
The purpose of this paper is to present a periodic averaging method for impulsive stochastic differential equations with Lévy noise under non-Lipschitz condition. It is shown that the solutions of impulsive stochastic differential equations with Lévy noise converge to the solutions of the corresponding averaged stochastic differential equations without impulses.
Uniform eventual practical stability of impulsive differential system in terms of two measures
Malaya Journal of Matematik, 2019
In the present paper, an impulsive differential system is investigated for uniform eventual practical stability. Sufficient criteria have been obtained for the uniform eventual practical stability of the impulsive differential system in terms of two measures by using Lyapunov-like function. The results that are obtained to investigate the stability are significantly dependent on the impulse moments. The results have been verified with the help of an example.
In this paper, we focus on the stability problems of first order linear impulsive differential equations. We construct an ordinary differential equation representation of the impulsive system such that it is suitable for the qualitative analysis of the later. This process is achieved by a transformation that bijectively maps the solutions of the initial value problems for impulsive differential equations to the solutions of the initial value problems for ordinary differential equations. A relationship between stability properties of impulsive differential equations and the corresponding ordinary differential equations was established.
Stochastic Impulsive Systems Driven by Renewal Processes
2005
Abstract— Stochastic impulsive systems are defined by a diffusion process with jumps triggered by a renewal process, i.e., the intervals between jumps are independent and identically distributed. We construct a model for such systems based on jump-diffusion equations and provide Lyapunov-based conditions that guarantee their mean-square stability. As an application, we show that stochastic impulsive systems can be used to model networked control systems with stochastic inter-sampling times and packet drops. Conditions for mean-square stability of the resulting systems are provided. For linear dynamics, these conditions can be formulated in terms of Linear Matrix Inequalities. We use two benchmark examples that previously appeared in the literature to illustrate the use of our results and to investigate their conservativeness. Keywords— Impulsive systems, Stochastic systems, Jump-diffusion processes, Renewal processes, Networked Control Systems
On the Averaging Principle for Systems of Stochastic Differential Equations
Mathematics of the USSR-Sbornik, 1991
New theorems are established about averaging of systems of Ito stochastic equations with coefficients measurable with respect to the "slow" variables, and about the limit behavior of a solution of the corresponding Cauchy problem for a singularly perturbed parabolic equation of second order. Bibliography: 15 titles.
Stability of impulsive systems driven by renewal processes
2009 American Control Conference, 2009
Necessary and sufficient conditions are provided for stochastic stability and mean exponential stability of impulsive systems with jumps triggered by a renewal process, that is, the intervals between jumps are independent and identically distributed. The conditions for stochastic stability can be efficiently tested in terms of the feasibility of a set of LMIs or in terms of an algebraic test. The relation between the different stability notions for this class of systems is also discussed. The results are illustrated through their application to the stability analysis of networked control systems. We present two benchmark examples for which one can guarantee stability for inter-sampling times roughly twice as large as in a previous paper.
A New Approach to Stability of Impulsive Differential Equations
m-hikari.com
In this work, new approach to stability theory of impulsive differential equations is proposed. Instead of putting all components of the state variable x in one Liapunov function, several functions of partial components of x, which can be much easier constructed, are used so that the ...
Stability criteria for impulsive Kolmogorov-type systems of nonautonomous differential equations
2012
In this paper we consider a class of impulsive Kolmogorovtype systems. The problems of uniform stability and uniform asymptotic stability of the solutions are studied. We establish stability criteria by employing piecewise continuous Lyapunov functions. Examples are given to demonstrate the effectiveness of the obtained results. We show, also, that the role of impulses in changing the behavior of impulsive models is very important.