Hybrid dynamical systems

TLDR

Hybrid systems combine continuous‑time and discrete‑time dynamics, and this article concentrates on robust stability and control rather than providing a comprehensive survey of the extensive literature. The tutorial aims to model hybrid system dynamics, review stability theory, and introduce hybrid control fundamentals. It focuses on analyzing asymptotic stability and designing robust stabilizing controllers that tolerate data perturbations, external disturbances, and measurement errors.

Abstract

Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.