Stabilisation of time-varying infinite delay control systems

Sufficient conditions are obtained for absolute stability of systems that are described by Lurie-type functional differential equations. It is assumed that the uncontrolled systems are unstable. The problem of Lurie consists of finding conditions for the feedback coefficients, and characterising the feedback function which make the trivial solutions of the functional differential equation stable. The author assumes that the system is completely controllable. The method is based on the use of Lyapunov functionals. A set of ´easily verifiable´ sufficient conditions on the roots of certain ´quasi-polynomial´ have been obtained. Systems of this kind are used for modelling a variety of control processes, including processes in biological systems.