Regional Pole Placement for Discrete-Time Systems Using Convex Approximations

This paper formulates the problem of allocating the closed loop poles of discrete-time systems in specific regions of the complex plane through state-feedback as a semi-definite optimization program. In order to handle the non-convex sets that arise from the minimum damping factor specification, a new inner approximation is proposed. Linear matrix inequalities (LMI) regions are used to define restrictions on the numerical algorithm. Finally, the method is compared to other alternatives and examples are given.