LMI approximation of pole-region for discrete-time linear dynamic systems

Pole-placement belongs to efficient tools in control system design, guaranteeing both stability and performance of closed loop system. In robust control design, so called LMI regions and the respective D-stability conditions have been developed recently. Concerning continuous-time systems, the pole regions respective to prescribed stability degree and damping factor are convex and can be directly described by LMIs. However, the discrete-time counterpart for the latter case is no more convex. In this paper, the inner convex approximation of discrete-time pole region for prescribed stability degree and damping factor is developed. The respective LMI region is then described and several examples are provided.