On positive realness, negative imaginariness, and H∞ control of state-space symmetric systems. (March 2019)

• Record Type: Journal Article
• Authors: Liu, Mei; Lam, James; Zhu, Bohao; Kwok, Ka-Wai
• Is Part Of: Automatica. Volume 101(2019)
• Page Start: 190
• Page End: 196
• Publication Date: 2019-03
• Subjects: H∞ control -- Negative imaginary systems -- Positive real systems -- State-space symmetry; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.11.031
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper studies positive realness and negative imaginariness of state-space symmetric systems. First, a necessary and sufficient condition is provided for a state-space symmetric system to be, respectively, positive real and negative imaginary. Then an explicit formulation for the infimum of H ∞ norm under a mixed H ∞ and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem. Finally, three examples are provided to illustrate the main results of the paper.