Behavioral realizations using companion matrices and the smith form
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hughes, TH
Abstract
Classical procedures for the realization of transfer functions are unable to represent uncontrollable behaviors. In this paper, we use companion matrices and the Smith form to derive explicit observable realizations for a general (not necessarily controllable) linear time-invariant behavior. We then exploit the properties of companion matrices to efficiently compute trajectories, and the solutions to Lyapunov equations, for the realizations obtained. The results are motivated by the important role played by uncontrollable behaviors in the context of physical systems such as passive electrical and mechanical networks.
Description
Keywords
behavioral theory, controllability, realization, linear systems, algebraic systems theory
Journal Title
SIAM Journal on Control and Optimization
Conference Name
Journal ISSN
0363-0129
1095-7138
1095-7138
Volume Title
54
Publisher
Society for Industrial & Applied Mathematics (SIAM)