scholarly journals Minimal realization of ℓ-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

2016 ◽  
Vol 2016 (10) ◽  
Author(s):  
Sergey Krivonos ◽  
Olaf Lechtenfeld ◽  
Alexander Sorin
Keyword(s):  
Minimal Realization ◽  
Galilei Algebra

scholarly journals On deformations of the Galilei algebra

2021 ◽  
Vol 2090 (1) ◽  
pp. 012066
Author(s):  
María Alejandra Alvarez ◽  
Javier Rosales-Gómez
Keyword(s):  
Lie Algebra ◽  
Galilei Algebra

Abstract In this note we compute all deformations of the 4-dimensional classical Galilei algebra &. In particular, we find examples of quadratic, cubic and quartic Lie algebra deformations.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

A minimal realization for affine control systems on connected Lie groups

2017 ◽  
Vol 14 (09) ◽  
pp. 1750126
Author(s):  
A. Kara Hansen ◽  
S. Selcuk Sutlu
Keyword(s):  
Control System ◽  
Control Systems ◽  
Lie Groups ◽  
Lie Group ◽  
Canonical Projection ◽  
Minimal Realization ◽  
Realization Problem ◽  
Affine Control Systems ◽  
Affine Control System ◽  
Connected Lie Group

In this work, we study minimal realization problem for an affine control system [Formula: see text] on a connected Lie group [Formula: see text]. We construct a minimal realization by using a canonical projection and by characterizing indistinguishable points of the system.

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