Hybrid Dynamical Systems

Modeling, Stability, and Robustness

Andrew R. Teel, Rafal Goebel, Ricardo G. Sanfelice, et al.

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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.

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Schlagwörter

State variable, Quasinorm, Algorithm, Lyapunov function, Dynamical system, Parameter, Special case, Parametrization, Norm (mathematics), Time domain, Without loss of generality, Local boundedness, Step function, Control theory, Limit point, Timer, Uniqueness, Differentiation under the integral sign, Linearization, Smoothness, Lyapunov stability, Quantity, Linear map, Notation, Hybrid automaton, Continuous function, Integrator, Differential equation, Boundedness, Hysteresis, Nonlinear system, Corollary, Differentiable function, Uniform convergence, Empty set, Stability theory, Approximation, Hausdorff distance, Lipschitz continuity, Absolute continuity, Hybrid system, Measurement, Theorem, Subsequence, Limit of a sequence, Convex set, Existential quantification, Compact space, Tangent cone, Monotonic function, Thyristor, Equilibrium point, Robustness, Differential inclusion, Uniform boundedness, Initial condition, Continuous function (set theory), Initial point, Variable (mathematics), Subset, Requirement, Smoothing, Infimum and supremum, Semi-continuity, Discrete time and continuous time, Limit superior and limit inferior, Flow map, Mathematical optimization, Regularization (mathematics), Symmetric matrix