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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. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Automatic control. --- Control theory. --- Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Dynamics --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Hermes solutions. --- Krasovskii regularization. --- Krasovskii solutions. --- Lyapunov conditions. --- Lyapunov functions. --- Lyapunov-like functions. --- asymptotic stability. --- closed sets. --- compact sets. --- conical approximation. --- conical hybrid system. --- continuity properties. --- continuous time. --- continuous-time systems. --- data structure. --- differential equations. --- differential inclusions. --- discrete time. --- discrete-time systems. --- dynamical systems. --- equilibrium points. --- flow map. --- flow set. --- generalized solutions. --- graphical convergence. --- hybrid arcs. --- hybrid control algorithms. --- hybrid dynamical systems. --- hybrid feedback control. --- hybrid models. --- hybrid system. --- hybrid time domains. --- invariance principles. --- jump map. --- jump set. --- modeling frameworks. --- modeling. --- nonlinear systems. --- numerical simulations. --- output function. --- pre-asymptotic stability. --- pre-asymptotically stable sets. --- precompact solutions. --- regularity properties. --- set convergence. --- set-valued analysis. --- set-valued mappings. --- smooth Lyapunov function. --- solution concept. --- stability theory. --- state measurement error. --- state perturbations. --- switching signals. --- switching systems. --- uniform asymptotic stability. --- well-posed hybrid systems. --- well-posed problems. --- well-posedness. --- ω-limit sets. --- Nonlinear control theory.