Revisiting minimal realizations [lecture notes]
M Kamaldar, S Sanjeevini… - IEEE Control Systems …, 2021 - ieeexplore.ieee.org
IEEE Control Systems Magazine, 2021•ieeexplore.ieee.org
Although realizations of transfer functions are a standard topic in textbooks about linear
systems theory, this article focuses on several points that are not widely treated. First, it is
shown that, for a given dynamics matrix A, the smallest number of sensors and actuators that
can be used to form a minimal realization is determined by properties of the Jordan form of
A. This leads to the notions of minimally sensed and minimally actuated systems. Next, the
rank of a transfer function is related to properties of the Jordan form of A and the rank of the …
systems theory, this article focuses on several points that are not widely treated. First, it is
shown that, for a given dynamics matrix A, the smallest number of sensors and actuators that
can be used to form a minimal realization is determined by properties of the Jordan form of
A. This leads to the notions of minimally sensed and minimally actuated systems. Next, the
rank of a transfer function is related to properties of the Jordan form of A and the rank of the …
Although realizations of transfer functions are a standard topic in textbooks about linear systems theory, this article focuses on several points that are not widely treated. First, it is shown that, for a given dynamics matrix A, the smallest number of sensors and actuators that can be used to form a minimal realization is determined by properties of the Jordan form of A. This leads to the notions of minimally sensed and minimally actuated systems. Next, the rank of a transfer function is related to properties of the Jordan form of A and the rank of the Rosenbrock system matrix.
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