On the stability of a class of nonlinear time delay systems

This paper focuses on some delay-dependent asymptotic stability problems for a special class of nonlinear systems: razionai systems with delayed states. Such systems may describe the behaviour of some population dynamics. Using a time-domain approach, we build an estimation of the stability regions (sufficient conditions) and show how to compute quadratic Liapunov functionals and functions for the corresponding analysis. The undelying idea is to use norms and Liapunov candidates defined on appropriate function or product spaces. Furthermore, in the synthesis case, we propose a memoryless state feedback controller which locally stabilizes the system. A numerical example (delayed van der Pol equation) is also considered. This paper generalizes some aspects presented in El Ghaoui and Scorletti [3] to a delay framework.