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
Hybrid Control Techniques for Switched-Mode DC-DC Converters Part I: The Step-Down Topology
A.G. Beccuti,Georgios Papafotiou,Manfred Morari,S. Almer,Hisaya Fujioka,Ulf Jönsson,Chung-Yao Kao,A. Wernrud,Anders Rantzer,M. Baja,Hervé Cormerais,Jean Buisson +11 more
TL;DR: Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem that involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down DC-DC converter.
Journal ArticleDOI
Modification to adaptive model reduction for regulation of distributed parameter systems with fast transients
TL;DR: In this paper, the output feedback control of distributed processes whose infinite dimensional representation in appropriate Hilbert subspaces can be decomposed to finite dimensional slow and infinite dimensional fast subsystems is addressed using a refined adaptive proper orthogonal decomposition (APOD) approach to recursively construct accurate low dimensional reduced order models.
Journal ArticleDOI
Switching Rule Design for Switched Dynamic Systems With Affine Vector Fields
TL;DR: The method deals with the class of switched systems where each mode of operation is represented by a dynamical system with an affine vector field and it guarantees global asymptotic stability of the tracking error dynamics.
Journal ArticleDOI
Hybrid Modeling of a DC-DC Series Resonant Converter: Direct Piecewise Affine Approach
TL;DR: A piecewise affine model is derived directly from the converter model based on analysis of the resonant converter on state plane trajectories, suitable for precise simulation and high performance controller design of resonant converters.
Journal ArticleDOI
A Maximum Principle for the Stability Analysis of Positive Bilinear Control Systems with Applications to Positive Linear Switched Systems
Lior Fainshil,Michael Margaliot +1 more
TL;DR: The main result is a first-order necessary condition for optimality in the form of a maximum principle (MP), which combines the standard needle variation with a basic result from the Perron--Frobenius theory of nonnegative matrices.
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.
Book
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.