In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite-dimensional linear dynamical system and an infinite-dimensional time delay operator, we show that...

We investigate the exponential stability of a linear system neutral-type with variable time lags. By using Newton–Leibniz formula and Lyapunov–Krasovskii functional, we prove two results on solutions. The criteria are stated in form matrix inequalities. MATLAB-Simulink software, present numerical examples illustrating applicability our assumptions. obtained extend generalize already known avail...

This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm proposed class systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These expressed in form linear matrix inequalities (LMI) which could be solved using solvers LMI Toolbox MATLAB. Two numerical examples to illustrat...

In this paper the stability of zero equilibrium a system with time delay is studied. The critical case multiple root characteristic equation linearized treated by applying Malkin type theorem and using complete Lyapunov-Krasovskii functional. An application to model for malaria under treatment considering action immune presented.

We consider a class of  systems of nonlinear  differential equations  neu tral type with distributed delay and periodic coefficients in the linear part. Using Lyapunov–Krasovskii functional, sufficient conditions for exponential stability zero solution are established estimates characterizing rate decay solutions at infinity, as well set attraction, obtained.

In this paper, a class of impulsive functional differential systems is investigated. It is proved that for the asymptotic stability of the zero solution of the system considered, it is sufficient that only some components of the right-hand side of the system are bounded for unbounded values of time. For functional differential equations without impulses, similar results were proved by Burton an...

In this contribution, the estimates for response of time-delay systems with nonlinear homogeneous right-hand side degree strictly greater than one are constructed. The existing results obtained via Lyapunov--Razumikhin approach reminded. Their proofs, revisited in appendix, lead to explicit expressions involved constants. Based on a recently introduced Lyapunov–Krasovskii functional and known d...

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...