Controller order reduction with pole region constraint

The problem of finding a low order output feedback dynamic controller for multi-input multi-output linear systems is considered. The resulting closed loop poles are placed within a pre-specified region in the complex plane. The matrix fraction descriptions of the plant and controller are parameterized using the eliminant matrix. The non-convex constraints imposed by the regional pole placement requirement on the resulting polynomial matrices, are convexified using a well known LMI based inner approximation method for polynomial stability region. The approximated convex problem is shown to be a semidefinite program solvable by standard optimization tools.