×

zbMATH — the first resource for mathematics

Observability canonical (phase-variable) form for non-linear time- variable systems. (English) Zbl 0546.93011
Summary: An observability canonical form for non-linear time-variable systems, \(\dot x=f(x,u,t)\), \(y=h(x,u,t)\), is introduced by analogy with the corresponding linear phase-variable forms. The transformation into observability canonical form follows from the non-linear observability map, whose Jacobian must be assumed to be a regular matrix in the considered domains of state x, input u and time t. If this observability matrix can be inverted analytically or numerically, the transformation into the observability canonical coordinates can be achieved directly. As opposed to linear systems, the non-linear observability canonical form with input depends, additionally, on the time derivatives of the input. This restricts a practical implementation.

MSC:
93B10 Canonical structure
93C10 Nonlinear systems in control theory
93C99 Model systems in control theory
93B07 Observability
93B17 Transformations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ACKERMANN J., Abtostregelung I, (1983)
[2] BESTLE D., Int. J. Control 38 pp 419– (1983) · Zbl 0521.93012
[3] BRANDIN V. N., Automrem. Control 36 pp 1595– (1976)
[4] FREUND E., Zeitvariable Mehrgrofien-systeme (1971)
[5] GAUTHTER J. P., I.E.E.E. Trans, autom. Control 26 pp 922– (1981) · Zbl 0553.93014
[6] HWANG M., J. optim. Theory Applic 10 pp 67– (1972) · Zbl 0226.93004
[7] KATLATH T., Linear Systems (1980)
[8] KRENER A. J., Systems Control Lett. 3 pp 47– (1983) · Zbl 0524.93030
[9] NIJMETJER H., Hie. Autom. 12 pp 50– (1981)
[10] SOMMER R., Regelungstechnik 27 pp 393– (1979)
[11] Su R., Proc. 22nd I.E.E.E. Conf. Decision and Control, (1983)
[12] ZEITZ M., Int. J. Control 37 pp 1449– (1983) · Zbl 0514.93012
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.