Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
R.A. Decarlo,Michael S. Branicky,Stefan Pettersson,Bengt Lennartson +3 more
- Vol. 88, Iss: 7, pp 1069-1082
TLDR
In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.Abstract:
This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.read more
Citations
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Journal ArticleDOI
Stability Criteria for Switched and Hybrid Systems
TL;DR: This paper considers the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws, and discusses the theory of Lyapunov functions and the existence of converse theorems.
Journal ArticleDOI
Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time
TL;DR: The stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts.
Journal ArticleDOI
Discrete abstractions of hybrid systems
TL;DR: It is shown that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic.
Book
Switched Linear Systems: Control and Design
Zhendong Sun,Shuzhi Sam Ge +1 more
TL;DR: In this paper, the authors propose a mathematical framework for stabilizing switching for autonomous systems, including controlability, observability, and normal forms, and feedback stabilization and optimization.
Journal ArticleDOI
Dynamical properties of hybrid automata
TL;DR: Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata and a class of hybrids whose solutions depend continuously on the initial state is characterized.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.