Simultaneous stabilization by static output feedback: a rank-constrained LMI approach

This paper presents a linear matrix inequality (LMI) approach to the design of a static output feedback controller that simultaneously stabilizes a finite collection of linear time-invariant systems. The problem is formulated as a novel rank-constrained LMI feasibility problem with a nonconvex rank condition, and is solved using an iterative penalty function method. Numerical experiments are performed to illustrate the proposed method

[1]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[2]  Stephen P. Boyd,et al.  Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices , 2003, Proceedings of the 2003 American Control Conference, 2003..

[3]  Dimitri Peaucelle,et al.  Ellipsoidal sets for resilient and robust static output-feedback , 2005, IEEE Transactions on Automatic Control.

[4]  Karolos M. Grigoriadis,et al.  A Unified Algebraic Approach To Control Design , 1997 .

[5]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[6]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[7]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[8]  S. Tarbouriech,et al.  Rank-one LMI approach to simultaneous stabilization of linear systems , 1999, 1999 European Control Conference (ECC).

[9]  Mario A. Rotea,et al.  On a sufficient condition for static output-feedback multimodel control , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[10]  John B. Moore,et al.  A Newton-like method for solving rank constrained linear matrix inequalities , 2006, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

[12]  John N. Tsitsiklis,et al.  A survey of computational complexity results in systems and control , 2000, Autom..

[13]  Joe H. Chow,et al.  Regional pole placement via low-order controllers with extensions to simultaneous stabilization , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[14]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[15]  Young-Hyun Moon,et al.  Design of a structurally constrained suboptimal controller using an LMI method , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[16]  James Lam,et al.  Simultaneous stabilization via static output feedback and state feedback , 1999, IEEE Trans. Autom. Control..

[17]  J. Murray,et al.  Fractional representation, algebraic geometry, and the simultaneous stabilization problem , 1982 .

[18]  Vincent D. Blondel,et al.  Simultaneous Stabilization Of Linear Systems , 1993 .