Keywords: Neural networks Time-varying delays Stability Lyapunov method a b s t r a c t This paper concerns the problem of delay-dependent stability criteria for neural networks with interval time-varying delays. First, by constructing a newly augmented Lyapunov– Krasovskii functional and combining with a reciprocally convex combination technique, less conservative stability criterion is establ...

We consider the simple random walk on Z evolving in a potential of independent and identically distributed random variables taking values in [0,+∞]. We give optimal conditions for the existence of the quenched point-to-point Lyapunov exponent, and for different versions of a shape theorem. The method of proof applies as well to first-passage percolation, and builds up on an approach of Cox and ...

The purpose of this paper is to establish discrete versions of the well-known Lyapunov’s stability theorem and LaSalle’s invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and cont...

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary ...

The goal of this paper is to establish the applicability of the Lyapunov-Schmidt reduction and the Centre Manifold Theorem for a class of hyperbolic partial differential equation models with nonlocal interaction terms describing the aggregation dynamics of animals/cells in a one-dimensional domain with periodic boundary conditions. We show the Fredholm property for the linear operator obtained ...

Until now, several methods have been developed to compute the domains of attraction for stationary points of polynomial non-linear systems. For the case of non-polynomial systems, though, this question is still open. In this paper a new method, based on Lyapunov’s stability theory and the theorem of Ehlich and Zeller, is presented for the computation of domains of attraction of non-polynomial s...

In this paper we propose a new procedure for construction of motor schema typically used in behaviour-based robotics. The procedure reverses the standard stability analysis approach by searching for a control function to fit a pre-defined Lyapunov function. In order to improve the applicability of this procedure, a new Second-Order extension to Lyapunov's Second Method is proposed, allowing a s...

This paper investigates the robust decentralized nonlinear control of power flow in a power system using a new configuration of UPFC. This structure comprises two shunt converters and one series capacitor called as hybrid power flow controller (HPFC). A controller is designed via control Lyapunov function (CLF) and adaptive observer to surmount the problems of stability such as tracking desired...

In this paper, the problem of dwell time for Hurwitz stability switched linear systems is considered. Dwell determined based on solution Lyapunov matrix equation differential systems. A numerical example illustrating efficiency theorem has been given.

In this paper, the synchronization of fractional-order uncertain delayed neural networks with an event-triggered communication scheme is investigated. By establishing a suitable Lyapunov–Krasovskii functional (LKF) and inequality techniques, sufficient conditions are obtained under which stable. The criteria given in terms linear matrix inequalities (LMIs). Based on drive–response concept, LMI ...