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 ...

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,...

We consider a class of algebraic Riccati equations arising in the study of positive linear time-delay systems. We show that this class admits diagonal positive definite solutions. This implies that exponentially stable positive linear timedelay systems possess Lyapunpov-Krasovskii functionals of a simple quadratic form. We also show that for this class of equations, the existence of positivedef...

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...

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...

This paper examines saturated control of a general class of uncertain nonlinear systems with timedelayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov–Krasovskii (LK) functionals is provided to prove uniformly ultimately bounded tracking despite un...

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 ...

Assessing stability of time-delay systems based on the Lyapunov-Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on the design of more and more involved class of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequal...

We propose an observer for a SIR epidemic model. The is then uplifted into predictor to compensate time delays in the input and output. Tuning criteria are given tuning gains of predictor, while estimation-error stability ensured using Lyapunov-Krasovskii functionals. predictor's performance evaluated combination with time-optimal control. show that nearly recovers level delay-free system.

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 ...