, Alexey Shumsky, Alexey Zhirabok
The algebraic approach known as functions’ algebra is used to develop the 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 non-smooth 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.
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