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Kaldmäe, Arvo; Kotta, Ülle; Shumsky, Alexey; Zhirabok, Alexey

Feedback linearization of possibly non-smooth systems. (English) Zbl 1382.93012

Proc. Est. Acad. Sci. 66, No. 2, 109-123 (2017).
Summary: The algebraic approach known as functions’ algebra is used to develop necessary and sufficient conditions for the existence of state transformation and static state feedback that linearize the system equations. The advantage of this method is that it allows considering also nonsmooth systems. The main object in functions’ algebra is the set of vector functions, divided into equivalence classes, which form a lattice. Both discrete- and continuous-time cases are considered. The solutions to the feedback linearization problem are expressed in terms of a finite sequence of vector functions, which contain all the independent functions having certain relative degrees. The theoretical results are illustrated by numerous examples.

Cited in 3 Documents

MSC:

93B18 Linearizations
93B25 Algebraic methods
93C55 Discrete-time control/observation systems
93B52 Feedback control
93C10 Nonlinear systems in control theory

Keywords:

nonlinear systems; feedback linearization; non-smooth functions; algebraic methods

Software:

NLControl
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Full Text: DOI
OA License

References:

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