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

作者：Forbes James Richard^*

来源：International Journal of Robust and Nonlinear Control, 2013, 23(8): 903-918.

DOI：10.1002/rnc.2808

• passivity-based control
• strictly positive real control
• linear matrix inequalities

The synthesis of controllers that minimize a H2 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 H2-norm is minimized and the controller is SPR. The first method retools the standard H2-optimal control problem by using a common Lyapunov matrix variable to satisfy both the H2 criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the H2 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.

• 出版日期2013-5-25