Fixed-structure LPV controller synthesis based on implicit input output representations

In this paper a novel LPV controller synthesis approach to design fixed-structure LPV controllers in input output (IO) form is presented. The LPV-IO model and the LPV-IO controller are assumed to depend affinely as well as statically on the scheduling variable. By using an implicit representation of the system model and the controller, an exact representation of the closed-loop behavior is achieved. Using Finsler's Lemma, novel stability conditions are derived in the form of linear matrix inequalities (LMIs). Based on these conditions a quadratic performance synthesis approach is introduced in form of bilinear matrix inequalities (BMIs) and solved using a DK-iteration based approach.

[1]  Jan C. Willems,et al.  The Behavioral Approach to Linear Parameter-Varying Systems , 2011, IEEE Transactions on Automatic Control.

[2]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[3]  Dimitri Peaucelle,et al.  Positive polynomial matrices and improved LMI robustness conditions , 2003, Autom..

[4]  S. O. Reza Moheimani,et al.  Perspectives in robust control , 2001 .

[6]  Roland Tóth,et al.  Fixed order LPV controller design for LPV models in input-output form , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  Didier Henrion,et al.  Polynomial LPV synthesis applied to turbofan engines , 2007 .

[8]  Herbert Werner,et al.  MIMO Controller Synthesis for LTI and LPV Systems Using Input-Output Models , 2011 .

[9]  R. Tóth,et al.  State-Space realization of LPV Input-Output models: practical methods for the user , 2010, Proceedings of the 2010 American Control Conference.

[10]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[11]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[12]  Hossam Seddik Abbas,et al.  Controller synthesis for input-output LPV models , 2010, 49th IEEE Conference on Decision and Control (CDC).

[13]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .

[14]  Carsten W. Scherer,et al.  LPV control and full block multipliers , 2001, Autom..

[15]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..