Abstract
be a continuous time or discrete time linear dynamical system of state space dimension n, with m inputs and with p outputs. (So that x CIr. n, u £~m, Y E IRp). Here the matrices F,G,H are supposed to be independant of time. We use L = m,n,p =~mn+np+n 2 to denote the space of all such systems, and we let L eo (resp. L er co,cr resp. Lm,n, p) denote the open and dense subspaces of all m,n,p' m,n,p completely observable (resp. completely reachable, resp. completely observable and completely reachable) systems. Base change in state space induces an action of GLn, the group of real invertible n x n matrices on Lm,n,p, viz-
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