Yuan, Y and Rai, A and Yeung, E and Stan, GB and Warnick, S and Gonçalves, J (2015) *A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems.* IEEE Transactions on Control of Network Systems, 4. pp. 301-311. ISSN 2325-5870

## Abstract

The dynamical structure function of a linear time invariant (LTI) system reveals causal dependencies among manifest variables without specifying any particular relationships among the unmeasured states of the system. As such, it is a useful representation for complex networks where a coarse description of global system structure is desired without detailing the intricacies of a full state realization. In this paper, we consider the problem of finding a minimal state realization for a given dynamical structure function. Interestingly, some dynamical structure functions require uncontrollable modes in their state realizations to deliver the desired input-output behavior while respecting a specified system structure. As a result, the minimal order necessary to realize a particular dynamical structure function may be greater than that necessary to realize its associated transfer function. Although finding a minimal realization for a given dynamical structure function is difficult in general, we present a straightforward procedure here that works for a simplified class of systems.

Item Type: | Article |
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Uncontrolled Keywords: | linear systems minimal realization theory systems biology |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Control |

Depositing User: | Cron Job |

Date Deposited: | 17 Jul 2017 19:01 |

Last Modified: | 21 Sep 2017 01:34 |

DOI: |