LMI-based controller synthesis: A unified formulation and solution

✍ Scribed by Izumi Masubuchi; Atsumi Ohara; Nobuhide Suda

• Book ID: 101282643
• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 169 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(19980715)8:8<669::aid-rnc337>3.0.co;2-w

✦ Synopsis

This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely-known LMIs (for H norm, H norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi-objective performance measures, which enable a new formulation of controller design through convex optimization.