A New Approach to the Design of Sampled--Data Dynamic Output Feedback Stabilizers

In this paper, a new methodology for the design of sampled--data dynamic output feedback stabilizers, by means of Lyapunov--Krasovskii functionals, for nonlinear systems with state--delays, is presented. The notion of Dynamic Output Steepest Descent Feedback (DOSDF), induced by a general class of Lyapunov-Krasovskii functionals, is introduced. Then it is shown that DOSDFs, no matter whether continuous or not, are stabilizers in the sampleandhold sense. The main advantage of the proposed methodology is that all kinds of discontinuities, in the function describing the DOSDF, are here accommodated. This fact greatly enlarges the possibilities of designing sampled--data dynamic output feedback stabilizers for nonlinear systems with state-delays. The inter-sampling system behavior as well as time-varying sampling intervals are taken into account. The stabilization in the sample-and-hold sense theory is used to prove the results. The proposed methodology is novel as well for the delay-free case, which is here dealt with as a special case.