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IMA Journal of Mathematical Control and Information 1998 15(2):155-183; doi:10.1093/imamci/15.2.155
© 1998 by Institute of Mathematics and its Applications
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A complete characterization of the feedback-linearized input–output response

P. N. PARASKEVOPOULOS, A. S. TSIRIKOS and D. KALOFONOS

Division of Computer Science, Department of Electrical and Computer Engineering, National Technical University of Athens 15773 Zographou, Athens, Greece

The problem of characterizing the feedback-linearized input–output response of a single-input single-output nonlinear system via static state feedback is completely solved. The proposed approach reduces the problem of determining the structure of the most general linearized input–output response, together with the respective control law, to that of solving a nonhomogeneous system of first-order partial differential equations. Necessary and sufficient conditions for this system of equations to have a solution are established which are of an algebraic nature and henceforth easily checkable. Based on these conditions, the linearized input–output response is completely characterized, prior to determining the desired control law. Furthermore, the general solution of this system of equations is derived which leads to the determination of the general analytical expression for the control law that satisfies the input–output linearization problem.


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