  The current paper presents a new approach to multilinear dynamical systems
analysis and control. The approach is based upon recent developments in tensor
decompositions and a newly defined algebra of circulants. In particular, it is
shown that under the right tensor multiplication operator, a third order tensor
can be written as a product of third order tensors that is analogous to a
traditional matrix eigenvalue decomposition where the "eigenvectors" become
eigenmatrices and the "eigenvalues" become eigen-tuples. This new development
allows for a proper tensor eigenvalue decomposition to be defined and has
natural extension to linear systems theory through a
\textit{tensor-exponential}. Through this framework we extend many of
traditional techniques used in linear system theory to their multilinear
counterpart.
