Báo Cáo Báo cáo hóa học ON STABILITY ZONES FOR DISCRETE-TIME PERIODIC LINEAR HAMILTONIAN SYSTEMS ˘ VLADIMIR

ON STABILITY ZONES FOR DISCRETE-TIME PERIODIC LINEAR HAMILTONIAN SYSTEMS ˘ VLADIMIR RASVAN Received 18 June 2004; Revised 8 September 2004; Accepted 13 September 2004


The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuousˇ time version, these results go back to Liapunov and Zukovskii; their deep generalizations are due to Kre˘n, Gel’fand, and Jakuboviˇ and obtaining the discrete version is not an ı c easy task since not all results migrate mutatis-mutandis from continuous time to discrete time, that is, from ordinary differential to difference equations.


Throughout the paper, the theory of the stability zones is performed for scalar (2nd-order) canonical systems. Using the characteristic function, the study of the stability zones is made in connection with the characteristic numbers of the periodic and skew-periodic boundary value problems for the canonical