Minimal state measurements for regional pole placement

The problem of minimizing the number of state measurements (and hence the number of sensors) required for placing the poles of a linear time invariant single input system with state feedback, is considered. It is assumed that only a subset of the closed loop poles are required to be placed in pre-specified locations in the complex plane. The remaining poles can assume any locations inside a pre-defined region in the complex plane. The resulting binary program with polynomial constraints is convexified using the theory of moments. Numerical examples illustrate the theory developed.