Strongly Absolute Stability Problem of Descriptor Systems

Article type: Research Article

Authors: Yang, Chunyu | Zhang, Qingling | Zhou, Linna

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

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.

Keywords: Lur'e type systems, descriptor systems, strongly absolute stability, linear matrix inequality (LMI)

Journal: Informatica, vol. 18, no. 2, pp. 305-320, 2007