Dual approaches to strictly positive real controller synthesis with a H 2 performance using linear matrix inequalities

• Published in: International journal of robust and nonlinear control Vol. 23; no. 8; p. 903
• Main Author: bes, James Richard
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2013
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.2808

SUMMARY The synthesis of controllers that minimize a H 2 performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state-feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed-loop H 2-norm is minimized and the controller is SPR. The first method retools the standard H 2-optimal control problem by using a common Lyapunov matrix variable to satisfy both the H 2 criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the H 2 performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd. [PUBLICATION ABSTRACT]