Robust ℋ∞ controller design for systems with hysteresis nonlinearities

Presents a design technique for robust control of systems having hysteresis nonlinearities using an LMI framework. Included also is an extension of recently developed stability criteria to remove the constant eigenspace associated with the multiplier used in the analysis procedure. This extension allows for the direct use of commonly available interior point methods to evaluate system stability and performance and subsequently to solve for the robust controllers. The resulting controllers are of reduced order since the additional states associated with the analysis have been eliminated. In this way there is no penalty for the stability guarantee. The effectiveness of the ℋ _∞ design procedure is illustrated with a simple loop shaping control problem for a non-minimum phase system