Stabilization of linear distributed control systems with unbounded delay
The authors study the stabilization of control systems modelled by an abstract retarded functional differential equation with infinite delay. The results reported in the paper extend those given by the first author in [Syst. Control Lett. 44, No. 1, 35--43 (2001; Zbl 0986.93057)] for the finite delay case. It is shown that if the poles of the controlled system located in the right half complex plane are finite and the translation semigroup is uniformly stable, then the stabilizing problem can be reduced to the stabilizing one for a finite-dimensional system. The equations under consideration model problems such as heat conduction in materials with memory or population dynamics for spatially distributed populations. An ample bibliography contains 51 items.
retarded functional differential equations
scientific article; zbMATH DE number 2174942
scientific article