Strongly Absolute Stability Problem of Descriptor Systems

  • Authors:

  • Chunyu Yang;Qingling Zhang;Linna Zhou

  • Affiliations:

  • Institute of Systems Science, Northeastern University, Shenyang, Liaoning province, 110004, P.R. China, e-mail: qlzhang@mail.neu.edu.cn;Institute of Systems Science, Northeastern University, Shenyang, Liaoning province, 110004, P.R. China, e-mail: qlzhang@mail.neu.edu.cn;Institute of Systems Science, Northeastern University, Shenyang, Liaoning province, 110004, P.R. China, e-mail: qlzhang@mail.neu.edu.cn

  • Venue:
  • Informatica
  • Year:
  • 2007

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Abstract

This paper considers Lur'e type descriptor systems (LDS). The concept of strongly absolute stability is defined for LDS and such a notion is a generalization of absolute stability for Lur'e type standard state-space systems (LSS). A reduced-order LSS is obtained by a standard coordinate transformation and it is shown that the strongly absolute stability of the LDS is equivalent to the absolute stability of the reduced-order LSS. By a generalized Lyapunov function, we derive an LMIs based strongly absolute stability criterion. Furthermore, we present the frequency-domain interpretation of the criterion, which shows that the criterion is a generalization of the classical circle criterion. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.