We consider an arbitrary number of interconnected nonlinear systems with time-delays and investigate them in view of input-to-state stability (ISS). The useful tools for single time-delay systems, the ISS Lyapunov-Razumikhin functions and ISS Lyapunov-Krasovskii functionals are redefined and applied to interconnected systems. By the help of a smallgain condition we prove that the whole system w...

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of illustrate the effectiveness of the proposed main results. Keywords—Neural networks, Lyapunov-Krasovskii, Time-varying

This paper considers the synchronization in complex networks with coupling delays, whose topologies could be be symmetric and asymmetric. Differing from most works on the synchronization in complex networks with coupling delays, this paper only uses a positivelydefined function, which is definitely not a Krasovskii-Lyapunov function, to analyze the synchronization criteria. Further, we can deri...

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...

In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by th...

The problem of the stability of a linear system with an interval time-varying delay is investigated. A new Lyapunov–Krasovskii functional that fully uses information about the lower bound of the time-varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov–Krasovskii functional can lead to less conservative results than some existing ones. Based on ...

A novel method based on Lyapunov-Krasovskii functionals for the stability analysis of linear systems with constant is introduced. The Lyapunov-Krasovskii functionals are provided using polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Examples show that these computationally tractable conditions can give tighter stability results than the ones in...