Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of ...

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...

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...

We propose an observer for a SIR epidemic model. The is then uplifted into predictor to compensate time delays in the input and output. Tuning criteria are given tuning gains of predictor, while estimation-error stability ensured using Lyapunov-Krasovskii functionals. predictor's performance evaluated combination with time-optimal control. show that nearly recovers level delay-free system.

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.