Reflection segments based stability domain approximation of the robust PID controller parameters

An innovative method for robust stabilizing PI,PD controller design and its stabilizing area approximation is presented for discrete-time SISO plants. It starts from 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 segments of two systems with different parameters are used to generate a rectangular and polygonal approximations of the stabilizing area of robust controller parameters that stabilize both systems.