The notion of homogeneity is extended to the time-delay nonlinear systems. Applications of Lyapunov-Krasovskii functionals and LyapunovRazumikhin functions for stability investigation are analyzed. The notion of local homogeneity is introduced, relations between stability/instability of the locally approximating dynamics and the original time-delay system are established. A link between homogen...

This paper focuses on the stabilization problem of neutral systems in the presence of control saturation. Based on a descriptor approach and the use of a modified sector condition, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions allow to consider systems presenting time-varying delays and are formulated directly as linear matrix ineq...

Systems with delays are a specific group of dynamic systems. The fact that some delays can be short and some can be long makes system analysis and control design much more complex. In this paper we present a proposal to solve the problem of stability and control design of continuous time systems with time-varying delays. Based on the Lyapunov-Krasovskii functional the stability condition is der...

In this paper, we investigate the delay-dependent robust stability of fuzzy Cohen-Grossberg neural networks with Markovian jumping parameter and mixed time varying delays by delay decomposition method. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing discrete delay interval into multiple subinterval, and choosing proper functionals with different weighting matr...

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin Krasovskii approaches, we propose novel control Lyapunov functions/functionals for problem barrier problem. The proposed extend existing ones from delay-free case to case, allow designing stabilizing controllers in closed-form. Since analytical solutions optimal are hard be achiev...

Stability analysis is a prerequisite and essential element of application and implementation processes in electrical and electronic fields [1]−[4]. Because time delays occur in many systems, including networked control systems, chemical processes, transportation systems, and neural networks, the issue of stability analysis for time-delay systems has received considerable attention during the la...

A nonlinear system of delay differential equations (DDEs) is considered. We obtain some new results on the asymptotic stability a zero solution considered by using well-known inequalities and Lyapunov–Krasovskii functionals. Two numerical examples illustrate applications obtained results. The presented make contributions to qualitative theory DDEs improve known from modern literature.