Regional pole and zero placement with static output feedback via the Modified Minimum Gain Lemma

This paper presents static output feedback controller synthesis methods that place closed-loop poles, blocking zeros, and transmission zeros within regions of the complex plane. In particular, closed-loop poles are placed within linear matrix inequality (LMI) regions of the complex plane, while closed-loop blocking and transmission zeros are placed in the open left-half plane (OLHP), and are thus minimum phase. An LMI formulation of the Modified Minimum Gain Lemma is used to ensure that the closed-loop system is minimum phase by forcing a nonzero minimum gain constraint. Two controller synthesis methods are presented, including Method 1, which places the closed-loop poles in the OLHP, and Method 2, which places closed-loop poles in the OLHP and closed-loop poles within a specified LMI region of the complex plane. Numerical examples are provided for both controller synthesis methods, with comparisons to controllers in the literature.