On the stability of linear canonical systems with periodic coefficients

Abstract

By a linear canonical system we mean a system of linear differential equations of the formwhereJis an invertible skew-Hermitian matrix andH(t) is a continuous Hermitian matrix valued function. We reserve the name Hami1tonia for real canonical systems withwhereIkdenotes thek×kunit matrix. In recent years the stability properties of Hamiltonian systems whose coefficient matrixH(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].