On Real Stable Pole Placement for Structured Systems Using Sturm and Sturm-Habicht Sequences

Abstract

During the last decades, many approaches for controller design of linear time-invariant systems have been developed. However, if a prescribed controller structure is desired, controller design may become more complicated. Typical examples include PID controllers and static output feedback. We propose a method for purely real pole or eigenvalue placement. Our approach is based on the closed-loop characteristic polynomial whose coefficients are polynomials in the controller parameters. We employ quantifier elimination to verify the existing conditions and to compute the controller gain.