This paper is concerned with systems of functional differential equations with either finite or infinite delay. We give conditions on the system and on a Liapunov function to ensure that the zero solution is asymptotically stable. Section 2 is devoted to finite delay, Section 3 to infinite delay, and Section 4 to examples. The remainder of this section introduces the problem for the finite dela...

This paper deals with the optimal control of a stochastic delay differential equation arising in the management of a pension fund with surplus. The problem is approached by the tool of the representation in infinite dimension. We show the equivalence between the 1-dimensional delay problem and the associated infinite dimensional problem without delay. Then we prove that the value function is co...

Whenever there is a time delay in a dynamical system, the study of stability becomes an infinite-dimensional problem. The centre manifold theorem, together with the classical Hopf bifurcation, is the most valuable approach for simplifying the infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions o...

The direct design of a linear phase R R one allows perfectly linear phase, but at the expense of the high filter order, N, and consecuently high computational burden for the given specification. IIR filters, however, can be designed with much smaller orders than their R R couterparts, but at the expense of the non-linear phase. It is, however, possible to design almost linearphase IIR filters f...