An LMI-Based Stability Analysis of Periodic Linear Time-Varying Systems: For General Cases Involving Higher Harmonic Frequencies

A necessary and sufficient condition for linear time-varying (LTV) systems to be exponentially stable has been given based on differential Lyapunov inequalities (DLIs). The exponential stability of an LTV system is guaranteed if the DLI for the system has a solution, however, few systematic methods have been reported for finding a solution of DLIs. We focus on a class of periodic LTV systems and propose a sufficient condition to find solutions of DLIs for the class by using linear matrix inequalities (LMIs). The proposed method allows that the systems may have higher harmonic frequencies. An example shows the effectiveness of the proposed analysis method.