Abstract
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). Some examples show the effectiveness of the proposed analysis method.
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