On the semi-definite programming solution of the least order dynamic output feedback synthesis

We show that a semi-definite programming approach can be adopted to determine the least order dynamic output feedback which stabilizes a given linear time invariant plant.

[1]  H. Kimura.  Pole assignment by gain output feedback , 1975 .

[2]  Z. Luo,et al.  Computational complexity of a problem arising in fixed order output feedback design , 1997 .

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

[4]  J. Rosenthal.  On Dynamic Feedback Compensation and Compactification of Systems , 1994 .

[5]  Carlos E. de Souza,et al.  A necessary and sufficient condition for output feedback stabilizability , 1995, Autom..

[6]  S. Kakutani.  A generalization of Brouwer’s fixed point theorem , 1941 .

[7]  Joachim Rosenthal,et al.  New results in pole assignment by real output feedback , 1992 .

[8]  G. Papavassilopoulos,et al.  On the rank minimization problem over a positive semidefinite linear matrix inequality , 1997, IEEE Trans. Autom. Control..

[9]  Nicos Karcanias,et al.  Global asymptotic linearisation of the pole placement map: a closed-form solution for the constant output feedback problem , 1995, Autom..

[10]  Arno Linnemann,et al.  A class of single-input single-output systems stabilizable by reduced-order controllers , 1988 .

[11]  D. Bernstein.  Some open problems in matrix theory arising in linear systems and control , 1992 .

[12]  R. Skelton,et al.  A complete solution to the general H∞ control problem: LMI existence conditions and state space formulas , 1993, 1993 American Control Conference.

[13]  A. Packard,et al.  Optimal, constant I/O similarity scaling for full-information and state-feedback control problems , 1992 .

[14]  B. Anderson,et al.  Output feedback stabilization—Solution by algebraic geometry methods , 1977, Proceedings of the IEEE.

[15]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[16]  R. Duffin,et al.  Series and parallel addition of matrices , 1969 .

[17]  Vincent D. Blondel,et al.  Survey on the State of Systems and Control , 1995, Eur. J. Control.

[18]  M. Mesbahi.  On the rank minimization problem and its control applications , 1998 .

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

[20]  P. Dorato,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[21]  Malcolm C. Smith.  On Minimal Order Stabilization of Single Loop Plants , 1986, 1986 American Control Conference.

[22]  R. Nikoukhah,et al.  LMITOOL: a package for LMI optimization , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[23]  A. Packard,et al.  A collection of robust control problems leading to LMIs , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[24]  Brian D. O. Anderson,et al.  Output Feedback and Generic Stabilizability , 1984 .

[25]  G. Papavassilopoulos,et al.  Bilinearity and complementarity in robust control , 1999 .

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

[27]  D. Bernstein,et al.  The optimal projection equations for fixed-order dynamic compensation , 1984 .

[28]  Karolos M. Grigoriadis,et al.  Fixed-order control design for LMI control problems using alternating projection methods , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[29]  J. Tsitsiklis,et al.  NP-Hardness of Some Linear Control Design Problems , 1997 .

[30]  K. Goh,et al.  Control system synthesis via bilinear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.