In this paper, the robust H∞ control problem is considered for uncertain neutral systems with discrete and distributed time delays. By using new Lyapunov-Krasovskii functionals, some sufficient conditions on H∞ robust performance analysis are given in terms of linear matrix inequalities (LMIs). Based on these conditions the dynamical output feedback controller are designed. Numerical examples a...

In this paper we discuss the practical stability of a class of time delay systems with an unstable equilibrium. We obtain sufficient conditions based on Lyapunov-Krasovskii functionals stated in terms of the feasibility of LMI’s. A “Practical” exponential estimate of the solution is also obtained. The result is extended to the practical stabilization and to the case of systems with multiple del...

The discrete-time delayed neural network with complex-valued linear threshold neurons is considered. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique and analysis method, several new delay-dependent criteria for checking the boundedness and global exponential stability are established. Illustrated examples are also given to show the ef...

A class of discrete-time nonlinear positive time-delay switched systems with sectortype nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov–Krasovskii functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence...

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...

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...

We consider a model of the single population dynamics described by delay differential equation. The asymptotic behavior solutions for this is studied in cases stability equilibrium points corresponding to complete extinction and constant positive size. In each case, Lyapunov–Krasovskii functionals are constructed, with help which estimates characterizing rate stabilization value obtained.

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of ...

Keywords: Continuous time difference systems Exponential stability Lyapunov–Krasovskii functionals a b s t r a c t This paper provides further Lyapunov results for the exponential stability of linear continuous time difference system involving discrete and distributed delays. We consider such a class of systems in the case when the discrete and distributed delays are independent thus completing...