A separation theorem for guaranteed H2 performance through matrix inequalities. (October 2018)

• Record Type: Journal Article
• Authors: Haesaert, Sofie; Weiland, Siep; Scherer, Carsten W.
• Is Part Of: Automatica. Volume 96(2018)
• Page Start: 306
• Page End: 313
• Publication Date: 2018-10
• Subjects: Separation of estimation and control -- H2-norm -- Matrix inequalities -- Linear time-invariant systems -- Discrete-time; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.07.002
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The usage of convex optimisation programs that leverage linear matrix inequalities allows for numerical solutions to the design of output-feedback controllers with guaranteed H 2 performance. As decreed by the classical separation theorem for the related LQG control problem, the H 2 control problem admits an optimal solution in terms of those of the separate optimal state-estimation and state-feedback design problems. This work details a new and alternative proof of this separation theorem. The proof builds on techniques for (linear) matrix inequalities and shows, in particular, that feasible but sub-optimal solutions of the state-feedback and the state-estimation problem yield a sub-optimal output feedback controller with guaranteed H 2 performance.