Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems.

Cover; Title; Copyright; Contents; Preface; 1 Introduction; 1.1 The modeling framework; 1.2 Examples in science and engineering; 1.3 Control system examples; 1.4 Connections to other modeling frameworks; 1.5 Notes; 2 The solution concept; 2.1 Data of a hybrid system; 2.2 Hybrid time domains and hybrid arcs; 2.3 Solutions and their basic properties; 2.4 Generators for classes of switching signals; 2.5 Notes; 3 Uniform asymptotic stability, an initial treatment; 3.1 Uniform global pre-asymptotic stability; 3.2 Lyapunov functions; 3.3 Relaxed Lyapunov conditions; 3.4 Stability from containment.

3.5 Equivalent characterizations3.6 Notes; 4 Perturbations and generalized solutions; 4.1 Differential and difference equations; 4.2 Systems with state perturbations; 4.3 Generalized solutions; 4.4 Measurement noise in feedback control; 4.5 Krasovskii solutions are Hermes solutions; 4.6 Notes; 5 Preliminaries from set-valued analysis; 5.1 Set convergence; 5.2 Set-valued mappings; 5.3 Graphical convergence of hybrid arcs; 5.4 Differential inclusions; 5.5 Notes; 6 Well-posed hybrid systems and their properties; 6.1 Nominally well-posed hybrid systems; 6.2 Basic assumptions on the data.

6.3 Con…