Delay-independent Stability Criteria Research Articles

Stability analysis for neural dynamics with time-varying delays

By using the usual additive neural-network model, a delay-independent stability criterion for neural dynamics with perturbations of time-varying delays is derived. We extend previously known results obtained by Gopalsamy and He to the time varying delay case, and present decay estimates of solutions of neural networks. The asymptotic stability is global in the state space of neuronal activations. From the techniques used in this paper, it is shown that our criterion ensures stability of neural dynamics even when the delay functions vary violently with time. Our approach provides an effective method for the stability analysis of neural dynamics with delays.

Stability Criteria for a Class of Feedback Controlled, Imperfectly Known, Bilinear Time-Delay Systems of the Neutral Type

A class of imperfectly known time-delay systems of the neutral type is considered in this paper. The uncertain systems are modelled as nonlinear perturbations to a known homogeneous-in-the-state bilinear system with state time-delay in the linear term; moreover, as well as being time and state dependent, the nonlinear perturbations are assumed to be state delay-dependent and input dependent. Using a Lyapunov-Krasovskiĭ functional, global uniform practical stability of the class of systems is investigated. To stabilize the imperfectly known systems, a class of robust memoryless feedback controls is designed and delay-independent stability criteria are presented for this problem. Une classe de systèmes de type neutre è retard imparfaitement connu est considéré dans cet article. Les systèmes incertains sont modélisés par des systémes bilinéaires connus homogènes en état avec un retard dans l'état du terme linéaire et en présence de perturbations non linéaires; en autre, en plus déetre dépendentes en temp et en état, les perturbations non lineaires sont supposées être dépendentes de l'état et de l'entrée. Utilisant une fonctionelle Lyapunov-Krasovskiĭ, la stabilité pratique uniformément globale est étudiée. Pour stabiliser les systèmes imparfaitement connus, une classe de contrôleur a boucle fermée robuste et sans mémoire est déterminée et des critères de stabilité non dépendent du retard sont présentés pour ce problème.

Delay-independent stability criteria for discrete uncertain large-scale systems with time delays

Based on the Lyapunov stability theorem associated with norm inequality techniques, the stability testing problem for discrete large-scale uncertain systems with time delays in the interconnections is investigated. Three classes of uncertainties are treated: nonlinear, linear unstructured and linear highly structured uncertainties. Several new delay-independent sufficient conditions, expressed by inequalities, are presented to preserve the asymptotic stability of the discrete large-scale uncertain time-delay systems. Although the Lyapunov stability theorem is utilized, it is not necessary to solve any Lyapunov equation. Two demonstrative examples are given to show the effectiveness of these quantitative results.

Delay-independent exponential stability criteria for time-varying discrete delay systems

Derives delay-independent exponential stability conditions for linear/nonlinear time-varying discrete delay systems. Since these conditions are of delay-independence and easily verifiable, they may provide handy tools for the stability analysis. >

Delay-independent stability criteria for neutral differential equations

Delay-independent stability criteria for neutral differential equations

Stability of x(t)=Ax(t)+Bx(t- tau )

A stability criterion for linear time-delay systems described by a differential difference equation of the form dx(t)=Ax(t)+Bx(t- tau ) is proposed. The result obtained includes information on the size of the delay and therefore can be a delay-dependent stability condition. Its relation to existing delay-independent stability criteria is also discussed. >

Delay-independent stability criteria for discrete-delay systems

Several sufficient conditions for stability of linear discrete-delay systems are derived. Since these conditions are independent of the delay and possess simple forms, they will provide useful tools to check stability of the systems at the first stage.