Symmetric linear systems: an application of algebraic systems theory
- 1 June 1983
- journal article
- research article
- Published by Taylor & Francis in International Journal of Control
- Vol. 37 (6) , 1371-1384
- https://doi.org/10.1080/00207178308933051
Abstract
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.Keywords
This publication has 3 references indexed in Scilit:
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- Linear Representations of Finite GroupsPublished by Springer Nature ,1977
- Discretized partial differential equations: Examples of control systems defined on modulesAutomatica, 1974