Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils
Christian Mehl · SIAM Journal on Matrix Analysis and Applications · 2000
In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils $\lambda S-H$, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur, for example, in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving transformations, i.e., J-congruence-transformations $(\lambda S-H) \mapsto -JP^{\ast}J(\lambda S-H)P$, where P is nonsingular or unitary.