Abstract:This talk will be in three parts.In the first part, we will discuss relaxed Lyapunov-based conditions to ensure input-to-state stability (ISS) of nonlinear time-delay systems. We will also present a systematic and constructive method to design a Lyapunov-Krasovskii functional for time-delay systems whose stability can be established via either the Razumikhin or the Halanay approach.The second part focuses on the rapid stabilization of general linear systems when the involved differential operator admits a Riesz basis of eigenvectors. We will present simple sufficient conditions for rapid stabilization and describe the relatively explicit construction of a feedback operator using an F-equivalence approach.In the final part, we will illustrate some applications of our results, namely within the framework of chemostat models with mortality, and for a chemical reactor model.
