Decentralized H2 Controller Design for Descriptor Systems: An LMI Approach;

This paper considers a decentralized H2 control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. Under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.

[1]  Guisheng Zhai,et al.  Decentralized H/sub /spl infin// controller design: an LMI approach , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[2]  Eiho Uezato,et al.  A Strict LMI Condition for H∞ Control of Descriptor Systems , 2000 .

[3]  George P. Papavassilopoulos,et al.  Numerical Experience with Parallel Algorithms for Solving the BMI Problem , 1996 .

[4]  T. Katayama,et al.  A generalized Lyapunov theorem for descriptor system , 1995 .

[5]  Low-order H/sub /spl infin// controller design for discrete-time linear systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[6]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  P. Shi.  On H∞ Control Design for Singular Continuous-Time Delay Systems with Parametric Uncertainties , 2004 .

[8]  D. Cobb,et al.  Descriptor variable systems and optimal state regulation , 1983 .

[9]  Guisheng Zhai,et al.  Decentralized Hinfinity controller design: a matrix inequality approach using a homotopy method , 1998, Autom..

[10]  G. Zhai,et al.  Decentralized H 8 Controller Design for Descriptor Systems , 2004 .

[11]  Guisheng Zhai,et al.  Centralized Design of Decentralized Stabilizing Controllers for Large-Scale Descriptor Systems , 2001 .

[12]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

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

[14]  Massimiliano Mattei,et al.  Sufficient conditions for the synthesis ofH? fixed-order controllers , 2000 .

[15]  Karolos M. Grigoriadis,et al.  Low-order control design for LMI problems using alternating projection methods , 1996, Autom..

[16]  E. Uezato,et al.  Strict LMI conditions for stability, robust stabilization, and H/sub /spl infin// control of descriptor systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[17]  G. Papavassilopoulos,et al.  A global optimization approach for the BMI problem , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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