A stability criterion for periodically time-varying systems

A generalized stability criterion for a periodically time-varying system is derived. It is shown that a time-varying system with the time-varying parameters having period T is stable if and only if the eigenvalues µ
i
of the state transition matrix at t = T, i.e., Φ(T), satisfy the condifio |µ
1
| < 1. The simple testing procedure is illustrated with the help of suitable examples.