Linear Symmetric Dynamical Systems

The problem of characterizing those linear systems that exhibit a symmetric behavior was completely solved in the 1D case, ten years ago, in a few papers by F. Fagnani and J. C. Willems. Unfortunately, that theory could not be extended in its full generality to multidimensional systems: the techniques used in the proofs limited the results to systems of independent equations and to a restricted class of symmetries. Using a recent result on symmetries of discrete systems, in this paper it is shown how to solve this open problem for other types of multidimensional systems, in particular, for systems of partial differential equations. Copyright c ©2005 IFAC.