1 Notes

Friedland [3, page 123] has the following remarks to offer on the method of feedback linearization: “The idea underlying feedback linearization is fairly obvious. The method probably was used for many years in practical control system design without anyone having reported it. Concurrently, a number of mathematical investigations on the use of differential geometry in dynamic systems wrere conducted without much notice by control system designers.” Our exposition of feedback linearization is based on the papers of Sommer [5] and Żak and MacCarley [8]. The research in applying diferential geometric methods to the control design intensified after the papers by Su [6], and by Hunt, Su and Meyer [4] appeared. Bakker and Nijmeijer [1] showed the equivalence of the Sommer’s approach and that of Hunt, Su and Meyer. Our treatment of the subject of state estimation follows the approach of Bestle and Zeitz [2], which in turn was presented, using the differential geometry notation, in the paper by Walcott, Corless and Żak [7]. Zeitz [9] offers a generalization of the method proposed by Walcott et al. [7].

References

[1] G. J. Bakker and H. Nijmeijer. Comments on ‘Control design for multivariable non-linear time-varying systems’. Int. J. Control, 41(6):1627–1629, 1985.

[2] D. Bestle and M. Zeitz. Canonical form observer design for non-linear time-variable systems. Int. J. Control, 38(2):419–431, 1983.

[3] B. Friedland. Advanced Control System Design. Prentice-Hall, Englewood Cliffs, New Jersey 07632, 1996.

[4] L. R. Hunt, R. Su, and G. Meyer. Global transformations of nonlinear systems. IEEE Transactions on Automatic Control, AC-28(1):24–31, January 1983.

[5] R. Sommer. Control design for multivariable non-linear time-varying systems. Int. J. Control, 31(5):883–891, 1980.

[6] R. Su. On the linear equivalents of nonlinear systems. Systems & Control Letters, 2(1):48–52, July 1982.

[7] B. L. Walcott, M. J. Corless, and S. H. Żak. Comparative study of non-linear stateobservation techniques. Int. J. Control, 45(6):2109–2132, 1987.

[8] S. H. Żak and C. A. MacCarley. State-feedback control of non-linear systems. Int. J. Control, 43(5):1497–1514, 1986.

[9] M. Zeitz. Comments on ‘Comparative study of non-linear state-observation techniques’. Int. J. Control, 46(5):1861–1863, 1987.