Wemake the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and ...

A mathematical driver model is given in the spacial equation form, which takes into account the previewed information of the path. Optimal control method is considered for the ideal no time-delay case and Lyapunov-Krasovskii functional approach is applied to deal with drivers’ reaction time-delay. For both cases, exponential stability is guaranteed for the closedloop system.

This paper studies the problem of robust exponential stability of uncertain perturbed neutral system with time varying delay. By introducing a novel Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs. Numerical examples are given to illustrate the theoretical developments.

This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. It is established that Filippov (Krasovskii) regularization of a switched system is contained within the convex hull of the Filippov (Krasovskii) regularizations of the subsystems. A common candidate Lyapunov function that has a negative semidefinite derivative along the trajectories of the subsystems is shown t...

This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. It is established that Filippov (Krasovskii) regularization of a switched system is contained within the convex hull of the Filippov (Krasovskii) regularizations of the subsystems. A common candidate Lyapunov function that has a negative semidefinite derivative along the trajectories of the subsystems is shown t...

This paper is concerned with the problem of exponential stability for a class of stochastic neural networks with Markovian switching and mode-dependent interval time-varying delays. A novel Lyapunov-Krasovskii functional is introduced with the idea of delay-partitioning, and a new exponential stability criterion is derived based on the new functional and free-weighting matrix method. This new c...

This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the “state” and norm bounded time varying quasi-linear uncertainties in the delayed “state” and in the difference operator. The stability analysis is performed via...

We consider a class of  nonautonomous  systems  differential  equations with time-varying concentrated and distributed  delays  than  can be unbounded.  Using Lyapunov–Krasovskii functional, some estimates of solutions are established. The obtained allow us to conclude whether the stable.