TY - JOUR
T1 - Robust decentralized H2 control of multi-channel descriptor systems with norm-bounded parametric uncertainties
AU - Weihua, Gui
AU - Ning, Chen
AU - Zhai, Guisheng
PY - 2009
Y1 - 2009
N2 - This paper considers a robust decentralized Hi 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 Hi 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.
AB - This paper considers a robust decentralized Hi 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 Hi 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.
KW - Decentralized control
KW - Descriptor systems
KW - Homotopy method
KW - Nonlinear matrix inequality
KW - Parametric uncertainty
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M3 - Article
AN - SCOPUS:66349130417
VL - 45
SP - 49
EP - 62
JO - Kybernetika
JF - Kybernetika
SN - 0023-5954
IS - 1
ER -