Extensions of Zubov's method for the determination of domains of attraction
thesisposted on 30.05.2018, 13:48 by Malik A. Hassan
This thesis is concerned with the extension of Zubov's method for the determination of domains of attraction. The basic definitions and theorems of Liapunov and Zubov as well as a numerical algorithm (due to White) are given in the introductory chapter. The application of the method of Zubov to some practical situations like power systems and control systems of order two is the subject of chapter two. Chapter three describes the determination of the domains of attraction for scalar time varying systems. The series solution has a similar problem of non-uniform convergence that occurs in autonomous systems. Extension of the method to third order non-linear autonomous systems is included in Chapter four so that it can be applied to second order time varying system which is described in Chapter five. Results in the form of slices or cross-sections of the stability boundaries in the various principal planes are obtained. Systems which have periodic solutions are examined and the domain of attraction of the stable limit cycle is determined in Chapter six. Approximate solutions are also used in trying to determine the domain of attraction of the periodic solutions. In Chapter seven a technique for solving global optimization problems is presented. Several one-dimensional and two-dimensional minimization problems are solved and the results indicate the accuracy of this technique.
Universiti Pertanian Malaysia (Serdang, Malaysia).
- Mathematical Sciences