Extended H2 output feedback control for continuous descriptor systems

This paper investigates the design of an “extended” H2 output feedback controller for continuous descriptor systems. In such problem, the controller, which is described within descriptor framework, has to satisfy simultaneously two conditions: 1-The closed-loop is admissible and has minimum H2 norm. 2-Only the internal stability of a part of the closed-loop is sought. In such case, the standard H2 output feedback control problem for descriptor systems cannot be solved. An explicit characterization of the optimal solution, based on two generalized algebraic Riccati equations (GAREs) and two structured generalized Sylvester-type equations, is given. A numerical example is included to illustrate the applicability of the proposed results.

[1]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[2]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[3]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[4]  Ali Saberi,et al.  Control of Linear Systems with Regulation and Input Constraints , 2000 .

[5]  Ali Saberi,et al.  Performance with regulation constraints , 2000, Autom..

[6]  Gjerrit Meinsma,et al.  Unstable and nonproper weights in H∞ control , 1995, Autom..

[7]  J. Krause.  Comments on Grimble's Comments on Stein's Comments on Rolloff of Ha Optimal Controllers , 1992 .

[8]  Kang-Zhi Liu,et al.  Solution to nonsingular H 2 optimal control problem with unstable weights , 1997 .

[9]  Michio Kono,et al.  Synthesis of servo mechanism problem via H ∞ control , 1992 .

[10]  Yoichi Hori,et al.  Mixed Sensitivity Optimization to Avoid Pole/Zero Cancellation , 1997, Autom..

[11]  Brian D. O. Anderson,et al.  Brief Extended H∞ control - H∞ control with unstable weights , 2000 .

[12]  João Yoshiyuki Ishihara,et al.  The full information and state feedback H2 optimal controllers for descriptor systems , 2003, Autom..

[13]  Kiyotsugu Takaba,et al.  H2 Output Feedback Control for Descriptor Systems , 1998, Autom..

[14]  Robert W. Newcomb,et al.  Some circuits and systems applications of semistate theory , 1989 .

[15]  James M. Krause.  Comments on Grimble's comments on Stein's comments on rolloff of H/sup infinity / optimal controllers , 1992 .

[16]  Xin Xin.  Reduced-order controllers for the Hinfinity control problem with unstable invariant zeros , 2004, Autom..

[17]  Kang-Zhi Liu,et al.  Parameterization of comprehensive stabilizing controllers and analysis of its structure , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[18]  Philippe Chevrel,et al.  AN EXTENDED STATE-FEEDBACK H2 CONTROLLER FOR DESCRIPTOR SYSTEMS , 2007 .

[19]  Luciano Pandolfi,et al.  Generalized control systems, boundary control systems, and delayed control systems , 1990, Math. Control. Signals Syst..

[20]  Philippe Chevrel.  Commande des systèmes linéaires , 2002 .

[21]  Takao Watanabe,et al.  LMI characterization of reduced-order H∞ controllers via invariant zero structure , 2003, Syst. Control. Lett..

[22]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .