State-space H controller design for descriptor systems

Masaki Inoue, Teruyo Wada, Masao Ikeda, Eiho Uezato

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Abstract This paper proposes a new linear matrix inequality (LMI) method to design state-space H controllers for linear time-invariant descriptor systems. Unlike preceding studies, where descriptor-type controllers are first computed and then numerically transformed to state-space controllers, the proposed method carries out the transformation analytically in the parameter domain. We derive a necessary and sufficient LMI condition for the existence of a state-space controller with the same dynamic order of the descriptor system to be controlled, which makes the closed-loop system regular, impulse-free, stable, and guarantees the H norm bound imposed on the closed-loop transfer function. Furthermore, we present parameterization of all such state-space controllers by variables satisfying the LMI condition and an arbitrary nonsingular matrix. The LMIs utilized in this paper are strict ones, that is, those containing no equality, while LMIs with equality constraints have been extensively used in the analysis and design for descriptor systems. The strict LMIs play key roles in deriving the results of this paper.

Original languageEnglish
Article number6439
Pages (from-to)164-170
Number of pages7
Publication statusPublished - 2015 Sept 1


  • Descriptor systems
  • Dynamic output feedback
  • H control
  • Linear matrix inequalities
  • State-space controllers

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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