An extended linearization approach to nonlinear system inversion

• Published in: IEEE transactions on automatic control Vol. 31; no. 8; pp. 725 - 733
• Main Author: Rugh, W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-08-1986; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Equations; Exact sciences and technology; Feedback control; Jacobian matrices; Linear systems; Military computing; Nonlinear systems; Performance analysis; State-space methods; System theory; Vents; Non linear system; Mathematical inversion; Linearization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.1986.1104385

The inversion problem for nonlinear systems is considered from both the internal viewpoint (state-equation representations) and the external viewpoint (Volterra-series representations). In order to circumvent difficulties in the known, exact inversion theory, a method for obtaining what will be called a partial inverse system is proposed. For a given nonlinear system, a cascade system, typically containing differentiators, is found such that the overall nonlinear system has a family of constant operating points with inputs and outputs identical. Furthermore, the linearization of the overall system about each of these constant operating points is the identity system.