On Some Approaches to Linearization of Affine Systems

Fetisov, D. A.

doi:10.1016/j.ifacol.2019.12.044

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…where 0 and are null and identity matrices, respectively. The transformation ( 7), ( 19) exists, if and only if: controllability matrix ( ) has full rank at ≥ 0 -= , is an integer If we suppose that the block canonical form has the form (6).…”

Section: Feedback Linearizationmentioning

confidence: 99%

“…The basic idea is to transform a nonlinear system into a linear one via nonlinear change of coordinates only (state linearization problem) or by nonlinear feedback and change of coordinates (feedback linearization problem) so that the linear control techniques can be applied [1]. Feedback linearization has been one of the most active research topics in recent years; linearization of affine systems [6], systems with nonsmooth nonlinearities [7], exact linearization [8]. Various methods exist to find feedback linearizable form for single input [9], and multi-input nonlinear systems [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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State feedback linearization using block companion similarity transformation

et al. 2021

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In this research work, a new method is proposed for linearizing a class of nonlinear multivariable system; where the number of inputs divides exactly the number of states. The idea of proposed method consists in representing the original nonlinear system into a state-dependent coefficient form and applying block similarity transformations that allow getting the linearized system in block companion form. Because the linearized system’s eigenstructure can determine system performance and robustness far more directly and explicitly than other indicators, the given class multivariable system is chosen. Examples are used to illustrate the application and show the effectiveness of the given approach.

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Section: Feedback Linearizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

State feedback linearization using block companion similarity transformation

et al. 2021

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A‐Orbital feedback linearization of multiinput control affine systems

Fetisov

2020

Intl J Robust & Nonlinear

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SummaryThis article deals with transformations of multiinput nonlinear control systems into linear controllable systems. For multiinput control affine systems, the notion of A‐orbital feedback linearizability is introduced which generalizes the notion of orbital feedback linearizability and is based on input‐dependent time scalings. A necessary and sufficient condition for A‐orbital feedback linearizability is derived for multiinput control affine systems. On the basis of this condition, an A‐orbital feedback linearization algorithm is developed. It is revealed that the proposed concept extends the existing approaches to orbital feedback linearization. More precisely, it is proved that if a system is A‐orbitally feedback linearizable in a neighborhood of some point, the dimension of the state is greater than that of the input by at least three, and the time scaling essentially depends on the input, then the system cannot be orbitally feedback linearized around that point.

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On feedback linearization of multi-input nonlinear control systems via time scaling and prolongation

Fetisov

2024

European Journal of Control

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On Some Approaches to Linearization of Affine Systems

Cited by 7 publications

References 14 publications

State feedback linearization using block companion similarity transformation

State feedback linearization using block companion similarity transformation

A‐Orbital feedback linearization of multiinput control affine systems

On feedback linearization of multi-input nonlinear control systems via time scaling and prolongation

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