# Orthogonal Representations for Output System Pairs

@article{Mullhaupt2018OrthogonalRF, title={Orthogonal Representations for Output System Pairs}, author={Andrew P. Mullhaupt and Kurt S. Riedel}, journal={ArXiv}, year={2018}, volume={abs/1803.06571} }

A new class of canonical forms is given proposed in which $(A, C)$ is in Hessenberg observer or Schur form and output normal: $\bf{I} - A^*A =C^*C$. Here, $C$ is the $d \times n$ measurement matrix and $A$ is the advance matrix. The $(C, A)$ stack is expressed as the product of $n$ orthogonal matrices, each of which depends on $d$ parameters. State updates require only ${\cal O}(nd)$ operations and derivatives of the system with respect to the parameters are fast and convenient to compute…

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