On a class of third order neutral delay differential equations with piecewise constant argument.
On absolute stability of nonlinear systems with small delays.
On delay-dependent robust stability under model transformation of some neutral systems
This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...
On delay-dependent stability for neutral delay-differential systems
This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.
On exponential stability of second order delay differential equations
We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method...
On generalized Wazewski and Lozinskii inequalities for semilinear abstract differential-delay equations.
On global exponential stability of discrete-time Hopfield neural networks with variable delays.
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations...
On partial stability for delay systems
On perturbations of deviations of periodic differential-difference equations in Banach spaces
On robust consensus of multi-agent systems with communication delays
In this paper, two robust consensus problems are considered for a multi-agent system with various disturbances. To achieve the robust consensus, two distributed control schemes for each agent, described by a second-order differential equation, are proposed. With the help of graph theory, the robust consensus stability of the multi-agent system with communication delays is obtained for both fixed and switching interconnection topologies. The results show the leaderless consensus can be achieved with...
On robust stability of neutral systems
This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.
On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations.
On stability and boundedness of solutions of a certain fourth-order delay differential equation.
On stability and oscillation of equations with a distributed delay which can be reduced to difference equations.
On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations
The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.
On stability of linear delay differential equations under Perron's condition.
On stability of linear neutral differential equations with variable delays
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays where and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
On the asymptotic stability of solutions of functional-differential equations
On the Dynamics of an Impulsive Model of Hematopoiesis
We propose and analyze a nonlinear mathematical model of hematopoiesis, describing the dynamics of stem cell population subject to impulsive perturbations. This is a system of two age-structured partial differential equations with impulses. By integrating these equations over the age, we obtain a system of two nonlinear impulsive differential equations with several discrete delays. This system describes the evolution of the total hematopoietic stem cell populations with impulses. We first examine...