Stability domain of fixed order controllers via reflection segments of polynomials

A novel randomized approach to fixed-order controller design is proposed for discrete-time SISO plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. The stability domain of a fixed order controller is defined as a set of stabilizing line segments generated by the set of stable reflection segments of the closed-loop system.