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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]