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...

In this paper, adaptive variable structure neural control is investigated for a class of SISO nonlinear systems in a Brunovsky form with state time-varying delays and unknown hysteresis input. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The effect of the unknown hysteresis with the Prandtl-Ishlinskii model is ...

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 note, we study the problem of asymptotic stability of the delay linear systems. More precisely, we examine the conservativity of a widely-used approach of investigation, based on quadratic Lyapunov-Krasovskii functionals. It is shown that the success of this approach implies strong delay-independent stability of the system under study, but is in general a still stronger condition. Also,...

Based on the Lyapunov–Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.  2005 Publi...

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 ...

A new method is proposed to determine the ultimate bounds and the convergence rates for perturbed timedelay systems when the Lyapunov–Krasovskii functionals and their derivatives are available. Compared with existing methods, the proposed method is more concise, more widely applicable, and the obtained results are less conservative. To show the three features, the proposed method is applied to ...

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stabi...

The robust stability of uncertain discrete-time recurrent neural networks with time-varying delay is investigated. By decomposing some connection weight matrices, new Lyapunov-Krasovskii functionals are constructed, and serial new improved stability criteria are derived. These criteria are formulated in the forms of linear matrix inequalities LMIs . Compared with some previous results, the new ...

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.