The asymptotic behavior of continuous dissipative systems and dissipative numerical integrators with fixed time-stepping can be fully investigated by Lyapunov-type theorem on continuous and discrete dynamical systems, respectively. However, once adaptive time-stepping is involved, such theories cease to work, and usually the dynamics should be investigated in a backward way, such as in terms of...

The stability of multi-input and multi-output networked control systems (MIMO NCS) is considered in this paper. A less conservative delay dependent stability criterion for MIMO NCS is proposed in terms of linear matrix inequality. The new result is obtained by taking the relationship between the delay upper bounds into account in Lyapunov functional, estimating the upper bound of the derivative...

In this paper, we consider the problem of robust delay-dependent stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. Less conservative stability criteria is put forward by using Lyapunov-Krasovskii functional approach. Based on delay-central point approach, introducing some free-weighting matrices and using tighter integral inequality for dealin...

This paper is considered with the robust stability problem for linear discretetime systems with polytopic uncertainty and an interval time-varying delay in the state. On the basis of a novel Lyapunov-Krasovskii functional, new delay-range-dependent stability criteria are established by employing the freeweighting matrix approach and a Jensen-type sum inequality. It is shown that the newly propo...

In this paper, asymptotical stability of genetic regulatory networks with interval time-varying delays is investigated. By choosing an appropriate new Lyapunov functional and employing convex combination method to estimate the derivative of the Lyapunov functional, some new delay-range-dependent and delay-derivativedependent/independent stability criteria are presented in terms of linear matrix...

In this article, we investigate the BV stability of 2×2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in BV. Our proof is based on a front tracking algorithm used to construct approximate...

In this paper, the global asymptotic stability of second-order neutral type Cohen-Grossberg neural networks with time-varying delays are investigated. First, by choosing properly variable substitution the system is transformed to first-order differential equation. Second, some sufficient conditions which can ensure the existence and global asymptotic stability of equilibrium point for the syste...

Many stability results in the theory of stochastic hereditary systems and their applications were obtained by construction of appropriate Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed by the authors during last decade for stability investigation of deterministic and stochastic functional-differential and difference equations. In this pa...

We exhibit a large class of Lyapunov functionals for nonlinear drift–diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic manyparticle systems, the zero-range process and the Ginzburg–Landau dynamics, which we describe briefly. We prove, as an application, linear inequalities between such an en...

In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dep...