Robust H∞ control based on LMIs of linear time-varying periodic systems

All of the issues 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 borrowing from the thought of solving robust control of the linear time invariant systems, the periodic problem is converted into a kind of norm bounded issues. The calculation of the state transition matrix of LTVP systems is avoided. The LMIs based memoryless state controllers of robust stabilization and H_∞ control of LTVP systems are designed. A numerical example is provided to demonstrate the application of the proposed methods.