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Feedback Linearization of Nonlinear Singularly Perturbed Systems with State-dependent Coefficients

Aleksey A. Kabanov
International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp.1743-1750, 2020

Abstract : The article examines a feedback linearization (FL) problem for a nonlinear singular perturbed (SP) system in a state-dependent coefficients form (SDC-form). The combination of the composite control technique of singular perturbation theory and a canonical similarity transformation approach for systems in a SDC-form are explored in this research. As a result, two FL problems for a fast state variables subsystem and a slow state variables subsystem are solved separately. The transformation matrix and feedback linearizing control for the entire nonlinear SP system are designed as a composition of solutions of these two FL problems. The composite stabilizing controller, based on feedback linearization and a pole placement method, is proposed for a nonlinear SP system in a SDC-form. Practical implementation of the proposed feedback linearizing composite stabilizing control is shown through an example (an inverted pendulum, controlled by a direct current motor).

Keyword : Feedback linearization, similarity transformation, singular perturbation, state-dependent coefficients

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