Output feedback based poles configuration for LDP systems with varying state and input dimensions

The problem of pole configuration via periodic output feedback for linear discrete periodic systems with time-varying dimensions of states and input spaces is addressed. By some mathematical derivation, the considered problem can be reduced into solving a special Sylvester matrix equation from which the periodic output feedback gains can be separated and computed explicitly. Based on this, a detail parametric algorithm is presented, by which countless periodic output feedback gains can be generated by choosing different free parameter matrices. Furthermore, the proposed approach is used to achieve robustness performance and robust poles configuration algorithm is provided. Numerical examples are employed to illustrate the effectiveness of the proposed algorithms.