This paper is devoted to the study of multi-agent consensus with a time-varying reference state in directed networks with both switching topology and constant time delay. Stability analysis is performed based on a proposed Lyapunov–Krasovskii function. Sufficient conditions based on linear matrix inequalities (LMIs) are given to guarantee multi-agent consensus on a time-vary reference state und...

In this article, stability and asymptotic properties of solutions of a real two-dimensional system x′(t) = A(t)x(t)+B(t)x(τ(t))+h(t, x(t), x(τ(t))) are studied, where A, B are matrix functions, h is a vector function and τ(t) ≤ t is a nonconstant delay which is absolutely continuous and satisfies lim t→∞ τ(t) = ∞. Generalization of results on stability of a two-dimensional differential system w...

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in te...

In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is red...

A Lyapunov–Krasovskii functional with prescribed derivative whose construction does not require the stability of system is introduced. It leads to presentation stability/instability theorems. By evaluating at initial conditions depending on fundamental matrix we are able present necessary and sufficient expressed exclusively in terms delay Lyapunov for integral systems. Some examples illustrate...

The discrete-time delayed neural network with complex-valued linear threshold neurons is considered. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique and analysis method, several new delay-dependent criteria for checking the boundedness and global exponential stability are established. Illustrated examples are also given to show the ef...

This work addresses the problems of robust exponential stability and stabilization for uncertain linear non-autonomous control systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of the Riccati differential equation approach and the Lyapunov-Krasovskii functional, new sufficient conditions are derived in terms of the solution of Riccat...

Abstract—In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness ...