Fixed order stabilizing controller design via random reflection segments

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. A novel approach is proposed for global and local optimization over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients.