This paper aims to study the existence and global stability of the periodic solutions to time-varying cell neural networks (CNN) with delays. By employing the Lyapunov function and inequality analysis method, the solution to this kind of delay CNN is proved to be bounded and therefore the existence criteria for its periodic solution is established. Moreover, by using Razumikhin technique, the g...

In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples ...

The present paper establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in di1erent forms for the given class of systems. Spec...

In this paper, we derive state-space integral quadratic constraints (IQC) equivalent to global performance criteria for a spatially invariant array of systems. We first show that a local IQC is equivalent to global stability with a decentralized Lyapunov function. Then, a local state-space IQC equivalent a global H∞ norm bound is also provided.

The stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. This paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (MDNN) and studies the stability of this algorithm. Also, stable learning algorithm for parameters of ...

In this paper we first study the problem of practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further the estimations of solution boundary and arrival time of the solution into a region are also investigated based on the practical stability results. Finally, the result on practical asymptotic stability is used to analyze the practical c...

We present a new comparison principle by introducing a notion of upper quasi-monotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle.

Abstract: This paper studies adaptive cluster synchronization of uncertain complex dynamical networks in finite time. Based on Lyapunov stability theorem and the finite-time control techniques, a useful criteria is established to guarantee the realization of adaptive cluster synchronization in finite time. Finally, a numerical example is given to illustrate the effectiveness and correctness of ...

A stochastic differential equation modeling an Internet congestion control model is investigated. By analyzing the Lyapunov exponent, invariant measure and singular boundary theory, some new criteria ensuring stochastic stability and bifurcation are obtained. Numerical simulation results are given to support the theoretical predictions.