Condensed forms of linear control system under output feedback (Q5935560)

The author presents two complementary condensed forms of linear control systems with output NEWLINE\[NEWLINE\dot{x}= A{\cdot}x + B{\cdot}u, \quad x \in \mathbb{R}^n, \;u \in \mathbb{R}^m,\qquad y= C{\cdot}x, \quad y \in \mathbb{R}^rNEWLINE\]NEWLINE under transformation of the state coordinates. The matrices \(B\) and \(C\) are of full rank. From them he derives two complementary condensed forms under output feedback. As an application of the condensed forms, the author shows that the output feedback control of the linear control systems generically reduces to a matrix completion problem, and he provides a partial solution to that problem, based on existing methods. All results are also valid for discrete control systems.