On Semi--Global Exponential Stability Under Sampling for Locally Lipschitz Time--Delay Systems

In this article, the stability preservation problem for locally Lipschitz nonlinear time-delay systems, by emulation of continuous-time dynamic output feedback controllers, is studied. Sufficient Lyapunov-like conditions are provided such that, by suitably fast sampling, the Euler emulation of continuous-time dynamic output feedback controllers ensures the semiglobal exponential stability of the related sampled-data closed-loop system. If other emulation schemes than the Euler one are used, practical semiglobal exponential stability is guaranteed, with arbitrarily small final target ball, by suitably fast sampling. The intersampling system behavior, as well as time-varying sampling intervals, is taken into account. In the provided results, the delay-free case is included as a special case. The practical applicability of the provided results is shown through the study of a nonlinear chemical reactor system with recycle and a glucose–insulin system.