SIAM Journal on Control and Optimization, Vol.52, No.5, 3053-3077, 2014
STABILIZATION IN THE SAMPLE-AND-HOLD SENSE OF NONLINEAR RETARDED SYSTEMS
In this paper, the problem of the stabilization in the sample-and-hold sense for fully nonlinear systems with an arbitrary number of arbitrary discrete as well as of distributed time delays is studied. It is shown that steepest descent feedbacks, continuous or not, induced by Lyapunov-Krasovskii functionals in a suitable (large) class, are stabilizers in the sample-and-hold sense. The fact that discontinuities are overcome by the sampling and holding process enlarges greatly the possibility of finding successful controllers for retarded nonlinear systems, by means of control Lyapunov-Krasovskii functionals.
Keywords:control Lyapunov-Krasovskii functionals;retarded functional differential equations;stabilization in the sample-and-hold sense