Parameterization of All Stabilizing Hc. Static State-Feedback Gains: Application to Output-Feedback Design

This paper presents a simplified parameterization of all Hinfin static state feedback controllers in terms of a single algebraic Riccati equation and a free parameter matrix. As a special case, necessary and sufficient conditions for the existence of an Hinfin static output feedback gain are given. An efficient computational algorithm is given. No initial stabilizing output feedback gain is needed. The technique is used to design an Hinfin lateral-directional command augmentation system for the F-16 aircraft

[1]  R. Skelton,et al.  Liapunov and covariance controllers , 1993 .

[2]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[3]  Tetsuya Iwasaki,et al.  All fixed-order H∞ controllers: observer-based structure and covariance bounds , 1995, IEEE Trans. Autom. Control..

[4]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[5]  Dante C. Youla,et al.  Modern Wiener-Hopf Design of Optimal Controllers. Part I , 1976 .

[6]  W. M. Wonham,et al.  Linear Multivariable Control , 1979 .

[7]  Karolos M. Grigoriadis,et al.  Covariance Controllers: A New Parameterization of the Class of All Stabilizing Controllers , 1990, 1990 American Control Conference.

[8]  Fang-Bo Yeh,et al.  Parametrization of nonlinear H/sub /spl infin// output feedback controllers-an algebraic approach via bounded real lemma , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[9]  Ben M. Chen.  Robust and H[∞] control , 2000 .

[10]  Tsutomu Mita,et al.  A complete and simple parametrization of controllers for a nonstandard H∞ control problem , 1998, Autom..

[11]  A. Isidori,et al.  Topics in Control Theory , 2004 .

[12]  Guoxiang Gu,et al.  Disturbance attenuation and H(infinity) optimization with linear output feedback control , 1994 .

[13]  Robert E. Skelton,et al.  Static output feedback controllers: stability and convexity , 1998, IEEE Trans. Autom. Control..

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

[15]  Hitay Özbay,et al.  On the strong stabilization and stable Hinfinity-controller design problems for MIMO systems , 2000, Autom..

[16]  Uri Shaked,et al.  An LPD approach to robust H2 and H∞ static output-feedback design , 2003, IEEE Trans. Autom. Control..

[17]  Kaiyang Yang,et al.  A Projective Algorithm for Static Output Feedback Stabilization , 2004 .

[18]  Vinicius Amaral Armentano,et al.  Structural constrained controllers for discrete-time linear systems , 1989 .

[19]  A. Weeren,et al.  The discrete time Riccati equation related to the H∞ control problem , 1992, 1992 American Control Conference.

[20]  Alessandro Astolfi,et al.  Static output feedback stabilization: from linear to nonlinear and back , 2001 .

[21]  Alessandro Astolfi,et al.  Static output feedback stabilization of linear and nonlinear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[22]  A. Weeren,et al.  The discrete-time Riccati equation related to the H∞ control problem , 1994, IEEE Trans. Autom. Control..

[23]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[24]  Daniel U. Campos-Delgado,et al.  A parametric optimization approach to H∞ and H2 strong stabilization , 2003, Autom..

[25]  Carsten W. Scherer,et al.  Computing optimal fixed order H∞-synthesis values by matrix sum of squares relaxations , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[26]  Robert E. Skelton,et al.  Covariance Controllers: A New Parameterization of the Class of All Stabilizing Controllers , 1990 .

[27]  V. Kučera.  Stability of Discrete Linear Feedback Systems , 1975 .

[28]  R. Skelton,et al.  Liapunov and Covariance Controllers , 1992, 1992 American Control Conference.

[29]  Kemin Zhou,et al.  On the parameterization H/sub infinity / controllers , 1992 .

[30]  Frank L. Lewis,et al.  Robot Manipulator Control: Theory and Practice , 2003 .

[31]  Yong-Yan Cao,et al.  A new necessary and sufficient condition for static output feedback stabilizability and comments on "Stabilization via static output feedback" , 1998, IEEE Trans. Autom. Control..

[32]  J. C. Geromel,et al.  Decentralised load-frequency control , 1985 .

[33]  Didier Henrion,et al.  Optimizing simultaneously over the numerator and denominator polynomials in the Youla-Kucera parametrization , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[34]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[35]  A. T. Neto,et al.  Stabilization via static output feedback , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[36]  V. Kučera,et al.  Discrete Linear Control: The Polynomial Equation Approach , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[37]  Jen-te Yu,et al.  A convergent algorithm for computing stabilizing static output feedback gains , 2004, IEEE Trans. Autom. Control..

[38]  Alessandro Astolfi,et al.  An algebraic characterization of the static output feedback stabilization problem , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[39]  Lihua Xie,et al.  On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers , 1992 .

[40]  Robert Skelton,et al.  A covariance control theory , 1985, 1985 24th IEEE Conference on Decision and Control.

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

[42]  Chi-Ming Yang,et al.  H∞ control for linear time-varying systems: controller parameterization , 1999, IEEE Trans. Autom. Control..

[43]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.