Stability and feedback control based on LMIs of linear time-varying periodic descriptor systems

All of the solutions of controllability, observability, stability and stabilization of linear time-varying periodic(LTVPD) system depend on its state transition matrix. However, it is very difficult to obtain the state transition matrix of an ordinary LTVPD 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 LTVPD systems is avoided. By introducing the definition of Riccati stability of LTVPD systems, the LMIs based memoryless state controllers of stabilization and robust stabilization of LTVPD systems are designed. Two numerical examples are provided to demonstrate the application of the proposed methods.