Robust decentralized H 2 control of multi-channel descriptor systems with norm-bounded parametric uncertainties

Weihua Gui; Ning Chen; Guisheng Zhai

Kybernetika (2009)

  • Volume: 45, Issue: 1, page 49-62
  • ISSN: 0023-5954

Abstract

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This paper considers a robust decentralized H 2 control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified H 2 norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method.

How to cite

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Gui, Weihua, Chen, Ning, and Zhai, Guisheng. "Robust decentralized $H_2$ control of multi-channel descriptor systems with norm-bounded parametric uncertainties." Kybernetika 45.1 (2009): 49-62. <http://eudml.org/doc/37663>.

@article{Gui2009,
abstract = {This paper considers a robust decentralized $H_2$ control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified $H_2$ norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method.},
author = {Gui, Weihua, Chen, Ning, Zhai, Guisheng},
journal = {Kybernetika},
keywords = {decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality; decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality},
language = {eng},
number = {1},
pages = {49-62},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust decentralized $H_2$ control of multi-channel descriptor systems with norm-bounded parametric uncertainties},
url = {http://eudml.org/doc/37663},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Gui, Weihua
AU - Chen, Ning
AU - Zhai, Guisheng
TI - Robust decentralized $H_2$ control of multi-channel descriptor systems with norm-bounded parametric uncertainties
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 1
SP - 49
EP - 62
AB - This paper considers a robust decentralized $H_2$ control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified $H_2$ norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method.
LA - eng
KW - decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality; decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality
UR - http://eudml.org/doc/37663
ER -

References

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  13. H 2 optimal control for descriptor systems, Acta Automat. Sinica 28 (2002), 6, 920–926 (in Chinese). 
  14. [unknown], R. Yu and D. Wang. (2003). On impulsive modes of linear singular systems subject to decentralized output feedback. IEEE Trans. Automat. Control 48 (2003), 1804–1809. MR2021433
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  16. Decentralized H 2 controller design for descriptor systems: An LMI approach, Nonlinear Dynamics and Systems Theory 6 (2006), 1, 98–108. MR2222782

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