Abstract:
This paper studies the problem for exponential stability of switched recurrent neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of argumented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a switching rule for exponential stability for of switched recurrent neural networks with interval time-varying delay is designed via linear matrix inequalities, and new sufficient conditions for the exponential stability of switched recurrent neural networks with interval time-varying delay via linear matrix inequalities(LMIs). A numerical example is given to illustrate the effectiveness of the obtained result.

Abstract:
This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Abstract:
We define Barna's polynomials as real polynomials with all real roots of which at least four are distinct. In this paper, we study the dynamics of Newton's functions of such polynomials. We also give the upper and lower bounds of the Hausdorff dimension of exceptional sets of these Newton's functions.

Abstract:
We study the multiplicativity factor and quadraticity factor for near quasinorm on certain sequence spaces of Maddox, namely, l(p) and l∞(p), where p=(pk) is a bounded sequence of positive real numbers.

Abstract:
We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x″(x[r](z))=c0z2

Abstract:
We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

Abstract:
This paper studies the problem of guaranteed cost control for a class of uncertaindelayed neural networks. The time delay is a continuous function belonging to a giveninterval but not necessary to be differentiable. A cost function is considered as anonlinear performance measure for the closed-loop system. The stabilizing controllersto be designed must satisfy some exponential stability constraints on the closed-looppoles. By constructing a set of augmented Lyapunov-Krasovskii functionals combinedwith Newton-Leibniz formula, a guaranteed cost controller is designed via memorylessstate feedback control, and new sufficient conditions for the existence of the guaranteedcost state feedback for the system are given in terms of linear matrix inequalities(LMIs). Numerical examples are given to illustrate the effectiveness of the obtainedresult.