All of the solutions of controllability, observability, stability and stabilization of linear time-varying
periodic(LTVP) system depend on its state transition matrix. However, it is very difficult to obtain the state transition matrix
of an ordinary LTVP system. By using the thought of solving robust control of the linear time invariant systems, the periodic
problem is converted into a kind of norm bounded problems. The calculation of the state transition matrix of LTVP systems
is avoided. The linear matrix inequalities(LMIs) based memoryless state controllers of stabilization and robust stabilization
of LTVP systems are designed. Two numerical examples are provided to demonstrate the effectiveness of the proposed
methods.