Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

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...

A nonautonomous system of ordinary differential equations is considered. This system has the zero solution, and there exists a nonnegative Lyapunov function which derivative is nonpositive. Theorems of the partial uniform stability and partial uniform asymptotic stability are proved. Copyright c ©2005 IFAC

The notion of non-uniform Robust Global Asymptotic Stability (RGAS) presented in this paper generalizes the notion of non-uniform in time RGAS for finiteor infinite-dimensional discrete-time systems. Lyapunov characterizations for this stability notion are provided. The results are applied to finitedimensional discrete-time systems obtained by time discretization of continuous-time systems by t...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

a chaos control method suggested by erjaee has been reviewed. it has been shown that thistechnique can be applied in various evolutionary systems of 2-dimensional types. the method has beenapplied for cases of the henon map, as well as burger’s map. the limitations of the control techniquehave also been discussed by considering the standard map and the gumowski-mira map. the resultsobtained thr...

in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.

We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for nonlinear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We...

Extremum seeking is a powerful control method to steer a dynamical system to an extremum of a partially unknown function. In this paper, we introduce extremum seeking systems on submanifolds in the Euclidian space. Using a trajectory approximation technique based on Lie brackets, we prove that uniform asymptotic stability of the so-called Lie bracket system on themanifold implies practical unif...

This paper investigates the uniqueness and globally uniformly asymptotic stability for a class of memristor-based recurrent neural networks with time-varying delays. By employing a homeomorphism and suitable Lyapunov functional and differential condition, a sufficient conclusion for the uniqueness and globally uniformly asymptotic stability of a class of memristor-based recurrent neural network...