# zbMATH — the first resource for mathematics

Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input. (English) Zbl 0772.93017
Summary: The transformation of nonlinear multi-input-multi-output systems $$\dot x=f(x,u)$$, $$y=h(x,u)$$ into an observer canonical form with reduced dependency on derivatives of the input is studied. Necessary and sufficient conditions for its existence and a straightforward algorithm for obtaining the canonical model are derived. The proposed method involves the solution of a nonlinear algebraic equation system and systems of first order linear partial differential equations. The nonlinear canonical form obtained permits global observer error linearization and it is a stage in the design of nonlinear observers. The method is illustrated by an example.

##### MSC:
 93B17 Transformations 93C15 Control/observation systems governed by ordinary differential equations 93B10 Canonical structure
Full Text:
##### References:
 [1] Bestle, D.; Zeitz, M., Canonical form observer design for non-linear time-variable systems, Int. J. control, 38, 419-431, (1983) · Zbl 0521.93012 [2] Birk, J.; Zeitz, M., Extended luenberger observer for non-linear multivariable systems, Int. J. control, 47, 1823-1836, (1988) · Zbl 0648.93022 [3] Isidori, A., () [4] Keller, H.; Keller, H., Automatisierungstechnik, Automatisierungstechnik, 34, 326-331, (1986) [5] Keller, H., () [6] Keller, H., Non-linear observer design by transformation into a generalized observer canonical form, Int. J. control, 46, 1915-1930, (1987) · Zbl 0634.93012 [7] Krener, A.J.; Isidori, A., Linearization by output injection and non-linear observers, Syst. and contr. lett., 3, 47-52, (1983) · Zbl 0524.93030 [8] Krener, A.J.; Respondek, W., Non-linear observers with linearizable error dynamics, SIAM J. control and opt., 23, 197-216, (1985) · Zbl 0569.93035 [9] Nijmeijer, H.; van der Schaft, A.J., () [10] Xia, X.; Gao, W., Non-linear observer design by observer error linearization, SIAM J. contr. and opt., 27, 199-216, (1989) · Zbl 0667.93014 [11] Zeitz, M., Observability canonical (phase-variable) form for non-linear time-variable systems, Int. J. syst. sci., 15, 949-958, (1984) · Zbl 0546.93011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.