In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive soluti...

This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the circle and Popov criteria is explained. Several examples are included to demonstrate the flexibility a...

This note studies the exponential stability of nonlinear stochastic systems with time delay. Firstly, a more general Lyapunov-Krasovskii functional is constructed, and based on Ito calculus rules for stochastic systems, a novel delay-dependent sufficient condition for exponential stability in mean square is derived in terms of linear matrix inequalities, and it is proved in theory that the obta...

In this paper, the problem of delay-dependent robust absolute stability of uncertain multiple time-delayed Lur'e systems with sector-bounded nonlinearity is investigated. The nonlinearity is assumed to be both time-invariant and time-varying. Based on the Lyapunov-Krasovskii stability theory and matrix decomposition method, some delay-dependent sufficient conditions for the robust absolute stab...

This paper deals with the absolute stability analysis for uncertain time delay Lur’e systems that have time-varying delays and sector and slope restricted nonlinearities. New delaydependent stability criteria are derived via linear matrix inequality (LMI) formulation that can be easily solved by various optimization techniques. Sector bounds and slope bounds are employed to the Lyapunov–Krasovs...

We investigate some stability problems in terms of twomeasures for nonlinear dynamic systems on time scales with fixedmoments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time sc...

This paper deals with a synchronization problem for a class of complex delayed dynamical networks with nonlinear coupling, including known and uncertain networks. Based on the Lyapunov stability theory, we propose controllers for both known and uncertain networks to realize synchronization. Numerical example is also given to illustrate the effectiveness of the proposed synchronization criteria.

This paper investigates the initial time difference equi-boundedness criteria in terms of two measures, initial time difference boundedness and Lagrange Stability in terms of two measures. These are unified with Lyapunov-like functions to establish a variational comparison result. We support our new results with analytic examples and numerical applications.

In this paper, a class of impulsive functional differential systems is investigated. It is proved that for the asymptotic stability of the zero solution of the system considered, it is sufficient that only some components of the right-hand side of the system are bounded for unbounded values of time. For functional differential equations without impulses, similar results were proved by Burton an...