Research, About The Absolute Stability Of The §Ý§å§â§Ó§Ö Control System

In this thesis, absolute stability of Lurie control systems is studied. We mainly discuss several common methods which ensure that the zero solution of Lurie control systems is absolute stability, and obtain some necessary and sufficient conditions or explicit algebraic criteria for absolute stability. The thesis contains five chapters: Chapter 1 is an introduction of the concept relating to absolute stability. It is first time that equivalence of two definitions about systems is proved; Chapter 2, Lurie's Method is considered. The root cause is analyzed in detail why sufficient conditions of absolute stability for direct control systems presented by previous researcher; in Chapter 3, S-procedure and its improvement is discussed practical algebraic criteria for absolute stability are given by using its improvement; Chapter 4, with the aid of popov's frequency criterion, necessary and sufficient conditions of absolute stability for some special Lurie control systems are obtained; in Chapter 5, we investigate the absolute stability of second and third order control systems in critical cases, in addition, we gain some algebraic criteria for absolute stability of several classes of special control systems which generalize or improve some known results by absolute stability with respect to partial variables.