An optimization approach to the pole-placement design of robust linear multivariable control systems

Traditional pole-placement methods for calculating state-feedback gains for multivariable regulators or tracking systems do not come with stability robustness guarantees. Even if good robustness happens to be obtained, pole-placement calculation of observer gains for observer-based control systems often results in poor stability margins. In this paper, a parameterization of all feedback gain matrices corresponding to a given set of specified closed-loop pole locations is derived. This parameterization is easily modified for observer gain matrices corresponding to a set of desired observer poles. The feedback or observer gain matrices are calculated by finding the parameters that maximize the H-infinity unstructured stability robustness norm for the given control system. Examples are given showing that the proposed approach yields state feedback regulators with good robustness (better than LQR) and is particularly effective for designing robust observer-based control systems.