Solution of Systems of Linear Ordinary Differential Equations with Periodic Coefficients

Systems of linear ordinary differential equations with periodic coefficients are assuming an increasing importance in engineering problems. Two applications of present interest are periodically time-variable networks and multimode waveguide with periodic physical distortions. Such applications have usually been analyzed by methods appropriate to special cases such as the second-order case or by approximate techniques valid for almost constant-parameter systems. However, perturbation techniques for almost stationary systems are inadequate for careful analysis of large-signal behavior of time-variable networks. Similarly, a periodically distorted helix waveguide, for which more than two modes must be considered, 1 should be described by a differential system of order greater than two. These examples illustrate the importance of a technique for obtaining essentially explicit solutions of periodic variable-parameter linear systems. Solutions in terms of characteristic exponents are known to exist for systems of linear differential equations with periodic coefficients." However, the methods usually