Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

The notion of homogeneity is extended to the time-delay nonlinear systems. It is shown that under some conditions the stability of homogeneous functional systems on a sphere implies the global stability of the system. The notion of local homogeneity is introduced, the relations between stability of the locally approximating dynamics and the original time-delay system are established. An example...