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Zbl 0546.93011
Zeitz, M.
Observability canonical (phase-variable) form for non-linear time- variable systems. (English)
[J] Int. J. Syst. Sci. 15, 949-958 (1984). ISSN 0020-7721; ISSN 1464-5319/e

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 2000:: *93B10 Canonical structure of systems
93C10 Nonlinear control systems
93C99 Control systems, guided systems
93B07 Observability
93B17 System transformation

Keywords: observability canonical form; non-linear time-variable systems; observability matrix

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