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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Proceedings ArticleDOI
On Switching between Motion and Force Control
TL;DR: A simple yet robust hysteresis-relay-based switching strategy is shown to be suitable for such type of motion control applications and the hybrid automaton, as most general tool, is used for exploring and analyzing the transients.
Journal ArticleDOI
A gradient algorithm for solution of the optimal control problem for hybrid switching systems
Journal ArticleDOI
Performance evaluation of holonic control of a switch arrival system
Carlos Indriago,Olivier Cardin,Odile Bellenguez-Morineau,Naly Rakoto,Pierre Castagna,Edgar Chacón +5 more
TL;DR: Evaluating the optimality and stability of the holonic control of a switch arrival system, a classical system where a unique server has to switch between leaking tanks full of fluids before they get empty, shows a good overall performance.
Proceedings ArticleDOI
Unifying behavior-based control design and hybrid stability theory
TL;DR: In this article, the authors describe the design and simulation implementation of a behavior-based control system using a command filtered, vector backstepping (CFBS) approach, which can be applied in designing a control system that can be used for maneuvering of nonholonomic robotic vehicles.
References
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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).
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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.