Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, A novel criterion for the global asymptotic stability of cellular neural networks with time-varying discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily...

This paper focuses on the characterization of delay effects on the asymptotic stability of some continuoustime delay systems encountered in modeling the posttransplantation dynamics of the immune response to chronic myelogenous leukemia. More explicitly, we shall discuss the stability of the crossing boundaries of the corresponding linearized models in the delay-parameter space. Weak, and stron...

For a class of uncertain nonlinear systems (UNSs), the flow-invariance of a timedependent rectangular set (TDRS) defines individual constraints for each component of the state-space trajectories. It is shown that the existence of the flowinvariance property is equivalent to the existence of positive solutions for some differential inequalities with constant coefficients (derived from the state-...

This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems. The conditions are derived from dissipativity analysis, and are based on the construction of piecewisequadratic functions via linear matrix inequalities (LM...

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 ...

This paper concerns the global stability of recently proposed laws for network congestion control. In earlier work it was shown that such laws were able to maintain local dynamic stability on networks of arbitrary delay, capacity and topology. In this paper we give conditions under which the stability can be shown to be global, focusing on the case of a single bottleneck network. The results in...

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 ...

The following notes contain the proof of Lyapunov’s theorem for stability and asymptotic stability of an equilibrium point of a nonlinear system, along with applications to the proof of asymptotic stability of an equilibrium point via linearization, plus some comments on unstable equilibrium points. The material is adapted from Fornasini & Marchesini, Appunti di teoria dei sistemi (in Italian);...

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations ...

This paper studies the asymptotic stability problem for a class of uncertain impulsive switched systems with discrete and distributed delays. Based on Lyapunov functional theory, delay-dependent sufficient LMI conditions are established for the asymptotic stability of the considered systems. Moreover, an appropriate feedback controller is constructed for stabilizing the corresponding closed-loo...