Stability of Lurie-type functional differential equations

Sufficient conditions are obtained for the absolute stability of systems that are described by Lurie-type functional differential equations. It is assumed that the uncontrolled system is unstable. The problem of Lurie consists of finding conditions for the feedback coefficients and characterizing the feedback function which makes the trivial solutions of the differential equation stable. It is assumed that the system is complete controllable. The method is based on the use of Lyapunov functionals. A set of ´easily verifiable´ sufficient conditions on the roots of certain ´quasi-polynomials´ are obtained