Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

129 Scopus Citations
View graph of relations


Related Research Unit(s)


Original languageEnglish
Pages (from-to)818-823
Journal / PublicationIEEE Transactions on Automatic Control
Issue number5
Publication statusPublished - May 2006


This note considers the generalized quadratic stability problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples. © 2006 IEEE.

Research Area(s)

  • Continuous-time, Generalized quadratic stability, Linear matrix inequality, Perturbation