Linearization by completely generalized input-output injection

López Morales, Virgilio   ; Plestan, F.   ; Glumineau, A.

Kybernetika, Tome 35 (1999) no. 6, pp. 793-802

Abstract (VO)

The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm and is based on the exterior differentiation.

Détail

Classification : 93B15, 93B18, 93C10
Keywords: linearization of nonlinear systems; input-output injection; exterior differentiation; I or O differential equation structure; observer synthesis

Bibliographie

[1] Bestle D., Zeitz M.: Canonical form observer design for nonlinear time varying systems. Internat. J. Control 38 (1983), 419–431 | DOI | MR

[2] Birk J., Zeitz M.: Extended Luenberger observers for nonlinear multivariable systems. Internat. J. Control 47 (1988), 1823–1836 | DOI | MR

[3] Chiasson J. N.: Nonlinear differential–geometric techniques for control of a series DC motor. IEEE Trans. Systems Technology 2 (1994), 35–42 | DOI

[4] Diop S., Grizzle J. W., Moraal P. E., Stefanopoulou A.: Interpolation and numerical differentiation for observer design. In: Proc. of American Control Conference 94, Evanston 1994, pp. 1329–1333

[5] Fliess M.: Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Trans. Automat. Control 35 (1990), 994–1001 | DOI | MR | Zbl

[6] Glumineau A., Moog C. H., Plestan F.: New algebro–geometric conditions for the linearization by input–output injection. IEEE Trans. Automat. Control 41 (1996), 598–603 | DOI | MR | Zbl

[7] Hammouri H., Gauthier J. P.: Bilinearization up to output injection. Systems Control Lett. 11 (1988), 139–149 | DOI | MR | Zbl

[8] Keller H.: Nonlinear observer design by transformation into a generalized observer canonical form. Internat. J. Control 46 (1987), 1915–1930 | DOI | MR | Zbl

[9] Krener A. J., Respondek W.: Nonlinear observers with linearizable error dynamics SIAM J. Control Optim. 23 (1985), 197–216 | DOI | MR

[10] López-M. V., Glumineau A.: Further results on linearization of nonlinear systems by input output injection. In: Proc. of 36th IEEE Conference on Decision and Control, San Diego 1997

[11] Marino R.: Adaptive observers for single output nonlinear systems. IEEE Trans. Automat. Control 35 (1990), 1054–1058 | DOI | MR | Zbl

[12] Marino R., Tomei P.: Dynamic output feedback linearization and global stabilization. Systems Control Lett. 17 (1991), 115–121 | DOI | MR | Zbl

[13] Phelps A. R.: On constructing nonlinear observers. SIAM J. Control Optim. 29 (1991), 516–534 | DOI | MR | Zbl

[14] Plestan F., Cherki B.: An observer for one flexible robot by an algebraic method. In: IFAC Workshop on New Trends in Design of Control Systems NTDCS’94, Smolenice 1994, pp. 41–46

[15] Plestan F., Glumineau A.: Linearization by generalized input–output injection. Systems Control Lett. 31 (1997), 115–128 | DOI | MR | Zbl

[16] Proychev T. Ph., Mishkov R. L.: Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input. Automatica 29 (1993), 495–498 | DOI | MR | Zbl

[17] Williamson D.: Observation of bilinear systems with application to biological systems. Automatica 13 (1977), 243–254 | DOI

[18] Xia X. H., Gao W. B.: Nonlinear observers design by dynamic error linearization. SIAM J. Control Optim. 27 (1989), 1, 199–216 | DOI | MR