Advanced gain scheduling techniques for the design of parameter-dependent observers

We present a systematic framework for the design of affine gain scheduled observers for affine LPV systems. The stability of the estimation error is based on the existence of an affine parameter-dependent Lyapunov function. The main contribution of the paper is the fact that the observer synthesis is formulated as a more easily tractable condition. This is achieved by the application of the multiconvexity concept and the introduction of a slack variable which eliminates the coupling between the observer matrices and the parameter-dependent Lyapunov function.

[1]  P. Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

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

[3]  U. Jonsson,et al.  A Popov criterion for systems with slowly time-varying parameters , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  Jamal Daafouz,et al.  State estimation for affine LPV systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[5]  Michael Athans,et al.  Analysis of gain scheduled control for nonlinear plants , 1990 .

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Pierre Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1998, IEEE Trans. Control. Syst. Technol..

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

[9]  Daniel J. Stilwell.  J-Q interpolation for gain scheduled controllers , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[11]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[12]  Tetsuya Iwasaki,et al.  LPV system analysis with quadratic separator , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[13]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[14]  Anders Helmersson,et al.  Methods for robust gain scheduling , 1995 .

[15]  D. Bernstein,et al.  Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis , 1995, IEEE Trans. Autom. Control..

[16]  Fen Wu.  An unified framework for LPV system analysis and control synthesis , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[17]  A. T. Neto.  Parameter dependent Lyapunov functions for a class of uncertain linear systems: an LMI approach , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[18]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[19]  S. Behtash,et al.  Design of controllers for linear parameter-varying systems by the gain scheduling technique , 1992 .

[20]  Wilson J. Rugh,et al.  Stability preserving interpolation methods for the synthesis of gain scheduled controllers , 2000, Autom..

[21]  Wilson J. Rugh,et al.  Interpolation of observer state feedback controllers for gain scheduling , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[22]  F. R. Gantmakher.  The Theory of Matrices , 1984 .