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Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 6, pp. 363370
DOI: 10.17587/mau.18.363-370


Feedback Linearization of Continuous and Discrete Multidimensional Systems

A. A. Kabanov, KabanovAleksey@gmail.com, Sevastopol State University, Sevastopol, 299053, Russian Federation

Corresponding author:Kabanov Aleksei A., PhD, Head of Department of Informatics and Control in Technical Systems, Sevastopol State University, Sevastopol, 299053, Russian Federation,
e-mail: KabanovAleksey@gmail.com

Received on February 08, 2017
Accepted on February 21, 2017

The problem of feedback linearization (FL) of continuous and discrete nonlinear MIMO systems is considered. The idea of FL method consists in converting the original nonlinear system into a linear one by means of feedback. Then, the methods of control theory for linear systems are used for system design. A widespread approach to FL design is based on the method of normal form, that uses a nonsingular transformation of system state variables z = T(x). In order to obtain a normal form of the nonlinear system in the neighbor of a some point, it is necessary to determine a special function the system virtual output, for which a relative degree (in the case of single input) or a vector relative degree (in the case of multiple input) is determined. Applicability of the normal form method for FL is provided by the conditions of controllability and involutivity for the considered nonlinear system, which are not always true. Moreover, when developing a linearizing control law, the main difficulty lies in the transition from transformed variables z to state variables x of the original system. In this paper, we propose another approach, based on representing the original nonlinear system into a state-dependent coefficient form and applying the canonical similarity transformation z = T(x)x, that allow getting the system to canonical form, that considerably simplifies the FL problem. Such similarity transformation allow accomplishing linearization of system without determining of the virtual system output. Mother advantage of the proposed method is that the technique of the transition from the transformed variables z to the state variables x of the original system is simpler. The results are illustrated by examples for continuous and discrete nonlinear systems.
Keywords: feedback linearization, multi-dimensional system, the canonical transformation

Acknowledgements: This work was supported by RFBR, project 15-08-06859.
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For citation:

Kabanov A. A. Feedback Linearization of Continuous and Discrete Multidimensional Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 6, pp. 363370.

DOI: 10.17587/mau.18.363-370

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