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...

In this paper, a dissipativity-based tracking problem is studied for the time-delay switched linear system with disturbances. First, composite disturbance observer designed to estimate nonlinear modeling disturbances and suppress external bounded energy. Then, eliminate adverse effects of on system, Lyapunov-Krasovskii functional designed, feasible conditions related are established. addition, ...

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is des...

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interv...

This paper deals with the problems of stability analysis and control synthesis with H∞ performance for the master-slave synchronization of Lur’e systems using a time-delay feedback control. The proposed approach consists in obtaining a new improvedH∞ robust stability criteria as well as a control law based on linear matrix inequalities (LMIs) via discretized Lyapunov–Krasovskii functional combi...

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new le...

The contribution focuses on the stability analysis of linear time-delay systems within the framework of the Lyapunov – Krasovskii functionals. The method used is based on the idea to check positive definiteness of the functionals exclusively on the specific Razumikhin-type set of functions. For the systems with incommensurate delays, it is proposed to use the modified functionals depend on the ...

This paper is devoted to stability analysis of linear systems with state delay and input saturation. The domain of attraction resulting from an a priori designed state feedback law is analyzed using Lyapunov–Razumikhin and Lyapunov–Krasovskii functional approach. Both delay-independent and delay-dependent estimation of the domain of attraction are presented using the linear matrix inequality te...

In this paper, we obtain an analytical Lyapunovbased stability conditions for scalar linear and nonlinear stochastic systems with discrete time-delay. The Lyapunov– Krasovskii and Lyapunov–Razumikhin methods are applied with techniques from stochastic calculus to obtain the regions of mean square asymptotic stability in the parameter space. Both delay-independent and delay-dependent stability c...

Time-dependent Lyapunov functionals appeared to be very efficient for sampled-data systems. Recently, new Lyapunov functionals were constructed for sampled-data control in the presence of a constant input delay. The construction of these functionals was based on Wirtinger’s inequality leading to simplified and efficient stability conditions in terms of linear matrix inequalities . In this artic...