The Hermann-Martin Curve

Grassmannian spectral shooting

“…The constructs and Grassmannian reductions we have considered in this paper, it turns out, have their origins in the control theory literature dating back to the early seventies, in particular in the pioneering papers of Hermann and Martin [44,45,46,47,48], Martin and Hermann [71] and Brockett and Byrnes [18]. We also found Bittanti, Laub and Willems [12], Lafortune and Winternitz [63], Rosenthal [87], Shayman [92] and Zelikin [100] particularly useful resources. A future direction we would like to explore is whether there are any applications of the numerical methods we have outlined here to practical non-autonomous control problems?…”

“…We also found Bittanti, Laub and Willems [12], Lafortune and Winternitz [63], Rosenthal [87], Shayman [92] and Zelikin [100] to be particularly useful resources. A future direction we would like to explore is whether there are any applications of the numerical methods we have outlined here to practical nonautonomous control problems?…”

“…For each property what is new, expected, proved, numerically observed, and its context? First, evolving the solution subspaces, considered as curves in the Grassmann manifold is not new for autonomous problems-see Hermann and Martin [44,45,46,47,48], Martin and Hermann [71] Brockett and Byrnes [18], Shayman [92], Rosenthal [87], Ravi, Rosenthal and Wang [86], Zelikin [100], Abou-Kandil, Freiling, Ionescu and Jank [1] and Bittanti, Laub and Willems [12]. Using Riccati systems to solve nonautonomous spectral problems is also not new-see Johnson [56], Hutson [51], Pryce [85], Manopoulous and Gray [69], Gray and Manopoulous [38] and Chou and Wyatt [23,24].…”