Zero dynamics of time-varying linear systems

Berger, Thomas GND; Ilchmann, Achim GND

The Byrnes-Isidori form with respect to the relative degree is studied for time-varying linear multi-input, multi-output systems. It is clarified in which sense this form is a normal form. (A,B)-invarianttime-varying subspaces are defined and the maximal(A,B)-invariant time-varying subspace included in the kernel of C is characterized. This is exploited to characterize the zero dynamics of the system. Finally, a high-gain derivative output feedback controller is introduced for the class of systems with higher relative degree and stable zero dynamics. All results are also new for time-invariant linear systems.

MSC 93C05, 93D15

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Berger, Thomas / Ilchmann, Achim: Zero dynamics of time-varying linear systems. 2010.

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