On the stability of linear canonical systems with periodic coefficients
W. A. Coppel, A Howe · Journal of the Australian Mathematical Society · 1965
By a linear canonical system we mean a system of linear differential equations of the form where J is an invertible skew-Hermitian matrix and H ( t ) is a continuous Hermitian matrix valued function. We reserve the name Hami1tonia for real canonical systems with where I k denotes the k × k unit matrix. In recent years the stability properties of Hamiltonian systems whose coefficient matrix H ( t ) is periodic have been deeply investigated, mainly by Russian authors ([2], [3], [5], [7]). An excellent survey of the literature is given in [6]. The purpose of the present paper is to extend this theory to canonical systems. The only work which we know of in this direction is a paper by Yakubovič [9].