Existence conditions of discrete-time strictly proper H∞ controllers

Presents sufficient and necessary conditions for discrete-time H_∞ control problems with strictly proper or fixed direct feedthrough matrix (FDFM) controllers based on a LMI approach. It is shown that there exists a strictly proper or FDFM H_∞ controllers if and only if the standard 3 LMIs condition as well as an additional dynamic one are solvable. The main results are more simple than some previous ones without any additional standard assumptions on the plants.