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Dual approaches to strictly positive real controller synthesis with a H 2 performance using linear matrix inequalities
Author(s) -
Forbes James Richard
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2808
Subject(s) - control theory (sociology) , linear matrix inequality , convex optimization , mathematical optimization , mathematics , controller (irrigation) , matrix (chemical analysis) , norm (philosophy) , computer science , regular polygon , control (management) , law , materials science , geometry , artificial intelligence , political science , agronomy , composite material , biology
SUMMARY The synthesis of controllers that minimize aH 2performance 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‐loopH 2 ‐norm is minimized and the controller is SPR. The first method retools the standardH 2 ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both theH 2criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with theH 2performance 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.