A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems
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.
Additional Information
© 2017 IEEE. Manuscript received June 24, 2015; revised September 7, 2015; accepted September 15, 2015. Date of publication November 5, 2015; date of current version June 16, 2017. This work was supported in part by the EPSRC under Projects EP/E02761X/1, EP/I03210X/1, and EP/I032223/1; in part by the Grants AFRL FA8750-09-2-0219, FA8750-11-1-0236, and DHS contract number HSHQDC-13-C-B0052. Recommended by Associate Editor S. Martinez.Additional details
- Eprint ID
- 78441
- DOI
- 10.1109/TCNS.2015.2498468
- Resolver ID
- CaltechAUTHORS:20170621-162121366
- EP/E02761X/1
- Engineering and Physical Sciences Research Council (EPSRC)
- EP/I03210X/1
- Engineering and Physical Sciences Research Council (EPSRC)
- EP/I032223/1
- Engineering and Physical Sciences Research Council (EPSRC)
- FA8750-09-2-0219
- Air Force Research Laboratory (AFRL)
- FA8750-11-1-0236
- Air Force Research Laboratory (AFRL)
- HSHQDC-13-C-B0052
- Department of Homeland Security
- Created
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2017-06-22Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field