This work studies certain perturbed and un-perturbed nonlinear systems of continuous discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method Lyapunov–Razumikhin (LRM), uniform asymptotic stability (UAS), (US), integrability boundedness solutions as well exponential (ES) instability are discussed. In this paper, five new theorems a corollary g...

Motivated by the fact that delay difference inclusions (DDIs) form a rich modeling class that includes, for example, uncertain time-delay systems and certain types of networked control systems, this paper provides a comprehensive collection of Lyapunov methods for DDIs. Firstly, the Lyapunov-Krasovskii approach, which is an extension of the classical Lyapunov theory to time-delay systems, is co...

This paper concentrates on the stability problem for linear systems with a differentiable time-varying delay via an auxiliary equation-based method. By supposing that second-order derivative of system state is available, equation obtained. On basis and equation, we define suitable delay-product-type augmented Lyapunov-Krasovskii functional (LKF), under which more information can be exploited. B...

This paper studies the stability analysis problem for time-varying delay systems. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed where its derivative a quadratic polynomial function of delay. A novel negative condition mentioned with two variable parameters developed to ensure that LKF negative, reducing conservatism on some similar results. Besides, an extended version Bess...

The stability problem of discrete-time linear systems with interval time-varying delays is investigated in this paper. According to the latest summation inequality technique, an improved free-matrix-based proposed In order make full use bound upper bounds difference Lyapunov-Krasovskii functional (LKF), augmented LKF some extra status information constructed. A new delay-range-dependent criteri...

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) proposed, which not only considers interaction between transmission delay and communication delay, but also takes interconnected relationship neutral into consideration. Then, two-sid...

In this paper, the synchronization of fractional-order uncertain delayed neural networks with an event-triggered communication scheme is investigated. By establishing a suitable Lyapunov–Krasovskii functional (LKF) and inequality techniques, sufficient conditions are obtained under which stable. The criteria given in terms linear matrix inequalities (LMIs). Based on drive–response concept, LMI ...

This paper is concerned with the stability of linear systems a time-varying delay. First, we derive new form constrained quadratic matrix inequality for reciprocally convex inequality. Second, an equivalent transform into inequality(LMI) derived. Third, upper bound time derivative Lyapunov Krasovskii functional(LKF), in matrix, obtained, and done to make it LMI. Finally, improvement shown throu...

Adaptive control using the ?-modification provides an easily implementable way to stabilize systems with uncertain or fluctuating parameters. Motivated by a specific application from neuroscience, we extend here this methodology nonlinear time-delay ruled globally Lipschitz dynamics. In order make result more handy in practice, provide explicit construction of Lyapunov–Krasovskii functional (LK...

In this paper, the problems of robust stabilization and H∞ control for uncertain stochastic systems with multiple time delays represented by the Takagi-Sugeno (T-S) fuzzy model have been studied. By constructing a new Lyapunov-Krasovskii functional (LKF) and using the bounding techniques, sufficient conditions for the delay-dependent robust stabilization and H∞ control scheme are presented in t...