Realization and canonical Presentation of Linear Systems through I/O Maps
Journal of the Franklin Institute
Place of Publication
In this paper, we use input and output maps to develop simple procedures to obtain minimal realizations for linear continuous-time systems. The procedures developed are numerically efficient and yield explicit formulae for the state-space matrices of the realization in terms of the system parameters, notably the system eigenvalues. Both systems with distinct eigenvalues and repeated eigenvalues are treated. We also present a procedure for transforming a realization obtained through the input or output map to Jordan canonical form. The transformation matrices required to transform the realization to Jordan canonical form are specified entirely in terms of the system eigenvalues. We illustrate the results obtained with several examples.
Hossein Oloomi and M.S. Fadali (2011).
Realization and canonical Presentation of Linear Systems through I/O Maps. Journal of the Franklin Institute.348 (2), 239-260. United Kingdom: Pergamon Press.