Stability analysis of continuous-time periodic systems via the harmonic analysis

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by the harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDLCP model whose transition matrix can be determined explicitly. By extending the Gerschgorin theorem to linear operators on the linear space , yet another disc-group criterion is derived, which is only sufficient. Stability of the lossy Mathieu equation is analyzed as a numerical example to illustrate the results.