# American Institute of Mathematical Sciences

March  2014, 4(1): 115-124. doi: 10.3934/mcrf.2014.4.115

## Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems

 1 Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE

Received  August 2012 Revised  December 2012 Published  December 2013

We give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems, consisting of distributional solutions $w$, that are periodic in the spatial variables, to a system of partial differential equations $$M\left(\frac{\partial}{\partial x_1},\cdots, \frac{\partial}{\partial x_d} , \frac{\partial}{\partial t}\right) w=0,$$ corresponding to a polynomial matrix $M\in ({\mathbb{C}}[\xi_1,\dots, \xi_d, \tau])^{m\times n}$.
Citation: Amol Sasane. Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems. Mathematical Control & Related Fields, 2014, 4 (1) : 115-124. doi: 10.3934/mcrf.2014.4.115
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