Cone reachability for linear differential systems

Abstract

Given a real nxn matrix A and a simplicial cone which is positively invariant under the linear differential system , we consider the problem of characterizing the closure of the set X_A(K) of all initial points x(0) ∈ Rⁿ which give rise to solutions x(t) that enter (and remain in) K. An explicit characterization of the closure of X_A(K) is given first in case A is diagon-able with a real spectrum. Subsequently a characterization for the closure of X_A(K) is given in case there exist k ∈ int K such that −Ak ∈ K, but in the absence of any other explicit assumptions on A.

¹This research was supported in part by USC-RPS Grant 130 E 132.

²This author was supported in part by NSERC Grant A4641.

¹This research was supported in part by USC-RPS Grant 130 E 132.

²This author was supported in part by NSERC Grant A4641.

Notes

¹This research was supported in part by USC-RPS Grant 130 E 132.

²This author was supported in part by NSERC Grant A4641.

Additional information

Notes on contributors

Michael Neumann

1

Ronald J. Stern

2