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2015 | OriginalPaper | Chapter

1. Introduction to LPV Systems

Author : Corentin Briat

Published in: Linear Parameter-Varying and Time-Delay Systems

Publisher: Springer Berlin Heidelberg

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Abstract

The goal of this chapter is to introduce the main ways for representing linear parameter-varying systems and emphasize their ability to represent a wide class of dynamical systems. A classification of the types of parameters regarding their mathematical properties and their physical meaning is also given. Several real world examples of LPV systems are finally discussed in order to demonstrate the relevance of the LPV framework.

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next chapter Stability of LPV Systems
Footnotes
1
For more details on dynamical systems, systems theory and related fundamental results, the reader should refer to [1‐4]. Additional details on LPV systems can also be found in [5‐7] and references therein.
 
2
A similar framework is based on Takagi-Sugeno systems where nonlinear systems can be represented as a state-dependent convex combination of linear time-invariant systems (polytopic system); see e.g. [27‐29].
 
3
These ideas have been successfully applied in the context of switching controllers, see e.g. the references [9, 34‐39].
 
4
Nonsingularity of \(A_{22}\) automatically implies that the system is regular and impulse-free [45]. These conditions imply that for any compatible initial condition, there exists a unique continuous solution to (1.20).
 
5
The convex hull of a set \(S\) is the smallest convex set containing \(S\).
 
6
Readers interested in a short history of robust control theory should read M. G. Safonov’s paper [51].
 
7
It is a particular case of the more general equality (A.3).
 
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Metadata
Title
Introduction to LPV Systems
Author
Corentin Briat
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Book
Linear Parameter-Varying and Time-Delay Systems

Print ISBN: 978-3-662-44049-0

Electronic ISBN: 978-3-662-44050-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-662-44050-6_1