STABILITY REGIONS OF LINEAR CANONICAL SYSTEMS WITH PERIODIC COEFFICIENTS

A new definition of the index of the stability region of a canonical s ystem of linear differential equations with periodic coefficients is p roposed. A simple proof of the Gel'fand-Lidskii theorem [1] on the str ucture of stability regions is given and a theorem on the directional convexity of such regions is proved. It follows from this theorem, in particular, that stability regions of parametric oscillations in a sys tem with a sign-definite Hamiltonian are convex with respect to the fr equency of parametric perturbation. (C) 1998 Elsevier Science Ltd. All rights reserved.