In this article, we study the uniform asymptotic stability of the switched system u′ = fν(t)(u), u ∈ Rn, where ν : R+ → {1, 2, . . . ,m} is an arbitrary piecewise constant function. We find criteria for the asymptotic stability of nonlinear systems. In particular, for slow and homogeneous systems, we prove that the asymptotic stability of each individual equation u′ = fp(u) (p ∈ {1, 2, . . . ,m...

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.

ABSTRACT. This paper studies impulsive discrete systems with time delay. Several criteria on uniform stability and uniform asymptotic stability are established by utilizing the Razumikhin technique. Both linear and nonlinear impulsive discrete systems with time delay are investigated. These stability criteria show that impulses can be used to stabilize a unstable system. Some numerical examples...

Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking systems. In this paper, a novel interpretation of extremum seeking is introduced.We show that the trajectories of an extremum seeking system can be approxim...

At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.

This paper studies uniform stability problems of stochastic impulsive systems by using a new comparison method. We firstly establish a comparison principle between the stochastic impulsive system and its scalar comparison system. Based on the obtained comparison result, uniform stability and uniform asymptotic stability of stochastic impulsive systems are established by analyzing those of compa...