Strongly absolute stability problem of descriptor systems: Circle criterion

This paper considers a Lur’e-type descriptor system (LDS) which is a feedback system whose forward path is a single-input and single-output linear time-invariant descriptor system and feedback path is an uncertain nonlinearity with sector constraint. The notion of strongly absolute stability is defined for LDS and some sufficient conditions are presented. If the forward path of LDS is impulsive free, the classical circle criterion (CC) for Lur’e-type standard systems (LSS) is shown to be still valid for LDS. If the forward path of LDS is not impulsive free, a new CC is derived by using a modified Nyquist stability condition. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.