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Erschienen in:
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2012 | OriginalPaper | Buchkapitel

1. An Overview of LPV Systems

verfasst von : Jeff S. Shamma

Erschienen in: Control of Linear Parameter Varying Systems with Applications

Verlag: Springer US

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Abstract

The framework of Linear Parameter Varying (LPV) systems concerns linear dynamical systems whose state-space representations depend on exogenous nonstationary parameters. Since its introduction by Shamma and Athans in 1988 to model gain-scheduling, the LPV paradigm has become a standard formalism in systems and controls, with many papers devoted to analysis, controller synthesis, and system identification of LPV models. This chapter reviews basic concepts and presents a representative selection of analytical approaches for LPV systems.

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Nächstes Kapitel Prediction-Error Identification of LPV Systems: Present and Beyond
Fußnoten
1
The now standard LPV acronym appears in [81] in 1992 and gained popularity with the works of [2,  3,  8,  11,  12,  61,  82], among others.
 
2
Boeing 747, F-14, F-16, and VAAC Harrier.
 
3
Whereas \(\mathcal{Q}\) denotes admissible trajectories for θ(⋅), the related Θ denotes admissible values of θ(t).
 
4
x denotes the Euclidean norm of x ∈ R n .
 
5
\(\left \Vert A\right \Vert\) denotes the induced matrix norm, \({\sup }_{x\not =0}\left \vert Ax\right \vert /\left \vert x\right \vert \).
 
6
For f : R → R n , \({\left \Vert f\right \Vert }_{2} ={ \left ({\int \nolimits \nolimits }_{0}^{\infty }f\mathrm{T}(t)f(t)\,\mathrm{d}t\right )}^{1/2}\).
 
8
For x ∞  = max1 ≤ i ≤ n x i for x ∈ R n . 
 
9
and personally gratifying.
 
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Metadaten
Titel
An Overview of LPV Systems
verfasst von
Jeff S. Shamma
Copyright-Jahr
2012
Verlag
Springer US
Buch
Control of Linear Parameter Varying Systems with Applications

Print ISBN: 978-1-4614-1832-0

Electronic ISBN: 978-1-4614-1833-7

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-1-4614-1833-7_1