This paper investigates the bounded input bounded output (BIBO) stability in a class of control system of nonlinear differential equations with time-delay. The proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear Volterra integral equations.
In this paper we give easily verifiable, but sharp (in most cases necessary and sufficient) algebraic conditions for the solutions of systems of higher order linear difference equations to be periodic. The main tool in our investigation is a transformation, recently introduced by the authors, which formulates a given higher order recursion as a first order… (More)
Consider the differential equation with deviating arguments (1) y(t)+PMt-o-l)-y(t-a2)] = 0 where p, 0\ and 172 are real numbers. We prove that every unbounded solution of (1) oscillates if and only if the characteristic equation (2) X+p(e-Áa<-e~x^) = 0 has no positive roots and 0 is a simple root of (2).
In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for a… (More)