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Almost periodic solutions for a weakly dissipated hybrid system
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
Amol Sasane 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 $M\in ({\mathbb{C}}[\xi_1,\dots, \xi_d, \tau])^{m\times n}$.
Keywords: controllability, distributions that are periodic in the spatial directions, Partial differential equations, autonomy, Fourier transformation, spatially invariant systems., behaviours.
Mathematics Subject Classification: Primary: 35A24; Secondary: 93B05, 93C2.
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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Amol Sasane