Incremental Graphical Asymptotic Stability for Hybrid Dynamical Systems

2017 ◽  
pp. 231-262
Author(s):  
Yuchun Li ◽  
Ricardo G. Sanfelice
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Hybrid Dynamical Systems

Hybrid Dynamical Systems

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Mathematical Analysis ◽  
Continuous Time ◽  
Hybrid Control ◽  
Control Algorithms ◽  
Hybrid Dynamical Systems ◽  
Approximation Techniques

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, this book 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.

scholarly journals The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109752
Author(s):  
Nathan J. Kong ◽  
J. Joe Payne ◽  
George Council ◽  
Aaron M. Johnson
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Kalman Filtering ◽  
Hybrid Dynamical Systems

scholarly journals Identification of a Class of Hybrid Dynamical Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 875-882
Author(s):  
Stefano Massaroli ◽  
Federico Califano ◽  
Angela Faragasso ◽  
Mattia Risiglione ◽  
Atsushi Yamashita ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Hybrid Dynamical Systems

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

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