FrAO 1-1 LMI optimization , for fixed-order H , controller design

A general H∞ controller design technique is proposed for scalar linear systems, based on properties of positive polynomial matrices. The order of the controller is fixed from the outset, independently of the order of the plant and weighting functions. A sufficient LMI condition is used to overcome non-convexity of the original design problem. The key design step, as well as the whole degrees of freedom are in the choice of a central polynomial, or desired closed-loop characteristic polynomial.

[1]  Huibert Kwakernaak,et al.  Robust control and H∞-optimization - Tutorial paper , 1993, Autom..

[2]  Alexandre Megretski,et al.  A convex parameterization of robustly stabilizing controllers , 1994, IEEE Trans. Autom. Control..

[3]  Karl J. Åström,et al.  Limitations on control system performance , 1997, 1997 European Control Conference (ECC).

[4]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Ioan Doré Landau,et al.  Combined pole placement/sensitivity function shaping method using convex optimization criteria , 1997, 1997 European Control Conference (ECC).

[6]  K.J. ÅSTRÖM,et al.  Design of PI Controllers based on Non-Convex Optimization , 1998, Autom..

[7]  J. William Helton,et al.  Classical control using H[∞] methods , 1998 .

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  Joe H. Chow,et al.  Low-order controller design for SISO systems using coprime factors and LMI , 2000, IEEE Trans. Autom. Control..

[10]  Dimitri Peaucelle,et al.  SEDUMI INTERFACE 1.02: a tool for solving LMI problems with SEDUMI , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[11]  Ryozo Nagamune.  Robust Control with Complexity Constraint : A Nevanlinna-Pick Interpolation Approach , 2002 .

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

[13]  Michael Sebek,et al.  Positive polynomials and robust stabilization with fixed-order controllers , 2003, IEEE Trans. Autom. Control..