This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily ...

In this research, we utilize Lyapunov functionals and obtain sufficient conditions for the stability of the zero solution of the discrete Volterra system of the form x(t+ 1) = Px(t) + t−1 ∑ s=t−r C(t, s)g(x(s)). Due to the nature of the Lyapunov functional, we will be able to show that all solutions are l ( [t0,∞) ∩ Z ) . AMS Subject Classifications: 3K20, 45J05.

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of fi...

Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for logconcave measures to superlinear potentials. Finally, we study ...

This paper considers the robust stability analysis problem for a class of uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the stochastic derivative of Lyapunov functionals, the novel asymptotic stability criteria are obatined in terms of Linear matrix inequalities (LMIs...

The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction which was proposed by V. Kolmanovskii and L. Shaikhet and successfully used already for functional differential equations, for difference equations with discrete time, for difference equations with continuous time, is used he...

In this paper, the stability analysis and control design of Takagi–Sugeno (TS) fuzzy systems subject to uncertain time-delay are addressed. The proposed approach is based on linear matrix inequalities and the Lyapunov–Krasovskii theory, where a new fuzzy weighting-dependent Lyapunov–Krasovskii functional is introduced. By employing the Gu discretization technique and strategies to add slack mat...

We derive decay rates for the energy of solutions of dissipative wave equations. The metod of proof combines multiplier techniques and the construction of suitable Lyapunov functionals. Without imposing any growth condition at the origin on the nonlinearity we show that this Lyapunov functional, which is equivalent to the energy of the system, is bounded above by the solution of a differential ...

We consider the class of closed generic fluid networks (GFN) models, which provides an abstract framework containing a wide variety of fluid networks. Within this framework a Lyapunov method for stability of GFN models was proposed by Ye and Chen. They proved that stability of a GFN model is equivalent to the existence of a functional on the set of paths that is decaying along paths. This resul...

This paper presents a new stability and L2-gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced by Naghshtabrizi et al. (Syst. Control Lett. 2008; 57:378–385; Proceedings 26th American Control Conference, New York, U.S.A., July 2007) in the framework of impulsive system representation. Most of the existing w...