Moduli and canonical forms for linear dynamical systems II: The topological case

@article{Hazewinkel2005ModuliAC,
  title={Moduli and canonical forms for linear dynamical systems II: The topological case},
  author={M. Hazewinkel},
  journal={Mathematical systems theory},
  year={2005},
  volume={10},
  pages={363-385}
}
  • M. Hazewinkel
  • Published 2005
  • Mathematics, Computer Science, Physics
  • Mathematical systems theory
    • AbstractIn this paper we study real linear dynamical systems $$\dot x = Fx + Gu,y = Hx,x \in R^n $$ = state space,u ∈Rm = input space,y ∈Rp = output space, under the equivalence relation induced by base change in state space; or in other words we study triples of matrices with real coefficients (F, G, H) of sizesn × n, n × m, p × n respectively, under the action(F, G, H.) →(TFT−1,TG, HT−1) ofGLn(R), the group of invertible realn × n matrices. One of the central questions studied is: “do there… CONTINUE READING
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    (R), x-> cf>ab(f(x)) fa: V~ x R"-> V~ x R
      ) denote the set of isomorphism classes of completely reachable families of linear systems (of dimensions (n, m, p)) over S. Now let/: S'-+ S be a continuous map
        ) iflab(s)aa(s)R(Fa,., Ga,)= R(F,(f(s)), G0 (f(s)))iJ 1 R(F)f(s))
          11) then mean that F
          • · p(R) be the n-vectorbundle obtained by glueing together the E, by means of the $
          8) implies that R(Fa,s• Ga.sl. has nonzero determinant)