Stefan M. Grünvogel (1998)
In: Z. Angew. Math. Mech. , 78 , pp. 927-928


If a semilinear control system possesses state space symmetry, there exist linear subspaces, which are invariant under every applied control. For the associated control system on projective space this means, that there exist invariant projective subspaces and therefore the system is not local accessible. On the first view this seems to be a disadvantage, because local accessibility is fundamental for the analysis of Lyapunov exponents, which determine the exponential stability properties. But it turns out, that we can restrict ourselves to the restricted control systems on these singular subspaces, because the whole Floquet and Morse spectrum (and therefore the Lyapunov spectrum) is attained on these subspaces.

Semilinear control systems with symmetry