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We present a novel approach to the exponential stability of switched functional differential equations. Our approach does not involve Lyapunov functions. It is simple and based upon spectral properties of Metzler matrices, a comparison principle and the average dwell-time technique. Consequently, some new explicit criteria for the exponential stability of switched functional differential equations are derived. Some illustrative examples are given. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

This work addresses the global exponential stability of nonlinear delayed discrete-time systems with Markovian switching. By a novel approach, some explicit criteria for the exponential stability in mean square of such systems are derived. An application to discrete-time neural networks is presented. [ABSTRACT FROM AUTHOR]

This work addresses the exponential stability in mean square of general neutral stochastic differential equations with delays. A simple approach to the exponential stability of the neutral stochastic differential equations with delays is proposed. Novel criteria for the exponential stability in mean square of such equations are presented. A comparison to existing results and an illustrative example are given. [ABSTRACT FROM AUTHOR]

Stochastic functional differential equations with infinite delay are considered. A novel approach to exponential stability of such equations is proposed. New criteria for the mean square exponential stability of general stochastic functional differential equations with infinite delay are presented. Illustrative examples are given. [ABSTRACT FROM AUTHOR]

Using a novel approach, we present some new scalar criteria for the uniform asymptotic stability of general nonlinear Volterra integro-differential equations. Discussion and illustrative examples of the obtained results are given. [ABSTRACT FROM AUTHOR]

By a novel approach, we present several new criteria for the mean square exponential stability of general non-linear stochastic delay differential equations. Both delay-independent and delay-dependent stability criteria are provided. A discussion of the obtained results is given. [ABSTRACT FROM AUTHOR]

General coupled functional differential-difference equations are considered. A new approach to exponential stability of such equations is presented. Consequently, some novel criteria for exponential stability of coupled functional differential-difference equations are given. As applications, the obtained results are used to derive explicit criteria for exponential stability of nonlinear functional differential equations of neutral type and those of singular delay differential equations. Some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

We present a novel approach to the mean square exponential stability of stochastic functional differential equations (SFDEqs). Consequently, new explicit criteria for the mean square exponential stability of SFDEqs are derived. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

General non-linear functional differential equations are considered. New explicit criteria for the exponential stability are presented. The stability criteria given in this paper include many existing results as particular cases. In particular, they unify, generalise and improve some ones published recently in [Ngoc, P. H. A. (2012). On exponential stability of non-linear differential systems with time-varying delay. Applied Mathematics Letters, 25(9), 1208–1213 and Ngoc, P. H. A. (2013b). Novel criteria for exponential stability of functional differential equations. Proceedings of the American Mathematical Society, 141(9), 3083–3091]. Two examples are given to show the effectiveness and advantage of the obtained results. [ABSTRACT FROM AUTHOR]

General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay. [ABSTRACT FROM AUTHOR]

By a novel approach, we give some explicit criteria for global exponential stability of singular nonlinear differential equations with delays. An application to electrical networks containing lossless transmission lines is presented. [ABSTRACT FROM AUTHOR]

General linear non-autonomous functional differential equations of neutral type are considered. A novel approach to exponential stability of neutral functional differential equations is presented. Consequently, explicit criteria are derived for exponential stability of linear non-autonomous functional differential equations of neutral type. A brief discussion to the obtained results and illustrative examples are given. [ABSTRACT FROM PUBLISHER]

General nonlinear time-varying differential systems with delay are considered. Several new explicit criteria for exponential stability are given. A discussion of the obtained results and two illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18, 909-939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks. [ABSTRACT FROM AUTHOR]

General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron-Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stability of positive equations is presented. Furthermore, two sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, we applied the obtained results to problems of the exponential asymptotic stability of Volterra integrodifferential equations. To the best of our knowledge, most of the results of this paper are new. [ABSTRACT FROM AUTHOR]

SUMMARY General nonlinear time-varying differential systems are considered. An explicit criterion for exponential stability is presented. Furthermore, an explicit robust stability bound for systems subjected to nonlinear time-varying perturbations is given. In particular, it is shown that the generalized Aizerman conjecture holds for positive linear systems. Some examples are given to illustrate obtained results.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

General nonlinear time-varying difference systems with time-varying delay are considered. Some new explicit criteria for global exponential stability are given. Two examples are given to illustrate the obtained results. [ABSTRACT FROM PUBLISHER]

We study stability radii of higher order linear difference systems under multi-perturbations. A formula for complex stability radius of higher order linear difference systems under multi-perturbations is given. Then, for the class of positive systems, we prove that the complex stability radius and real stability radius of the system under multi-perturbations coincide and they are computed via a simple formula. These are extensions of corresponding results of Hinrichsen and Son, Hinrichsen et al., Ngoc and Son, and Pappas and Hinrichsen. An example is given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study stability radii of linear systems under multi-perturbation of the coefficient matrices. Formulas for complex stability radius are derived. We then consider linear positive systems and prove that for this class of systems, the complex stability radius is equal to the real stability radius which can be computed via a simple formula. We illustrated the obtained results by two examples. [ABSTRACT FROM AUTHOR]