Robust decentralized H2 control of multi-channel descriptor systems with norm-bounded parametric uncertainties

Gui Weihua, Chen Ning, Guisheng Zhai

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)49-62
Number of pages14
Issue number1
Publication statusPublished - 2009
Externally publishedYes


  • Decentralized control
  • Descriptor systems
  • Homotopy method
  • Nonlinear matrix inequality
  • Parametric uncertainty

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Information Systems
  • Artificial Intelligence
  • Electrical and Electronic Engineering


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