دانلود کتاب Stability Theory by Liapunov's Second Method

In this monograph, I shall discuss the stability and boundednessof solutions of differential equations and related topics; theunderlying theme and connective thread being Liapunov's secondmethod. I have attempted to give an introduction to Liapunov'ssecond method which incorporates recent modifications and illustratesthe scope and power of this method.There is a vast literature on the theory and applications ofLiapunov's second method, and due to the nature of this seriesand the resultant restrictions in size, I have emphasized the derivationand application of stability criteria for ordinary differentialequations. As in any monograph of this nature, the selection oftopics has also been dictated by the interests of the author.Liapunov's second method is also an important tool in thetheory of control systems, dynamical systems and functional-differentialequations. Since an excellent book on stability theory incontrol systems has been published recently by Lefschetz [79], Ihave omitted all statements on control systems. For the stabilityin control systems, see [72], [74], [78]-[80], [153]. For dynamicalsystems, there are many interesting investigations [8]-[10], [15],[76], [103], [152], but dynamical systems are briefly treated inSection 22. Functional-differential equations are considered inChapter VIII where a Liapunov function is generalized to a Liapunovfunctional and similar results are discussed.There are two excellent English language books on this subj~ct; an introductory one by LaSalle and Lefschetz [74], and oneby Hahn [37]. Also, the outstanding books by Krasovskii [62]and Zubov [152] are now available in English translations.The first chapter gives background material and introducesLiapunov's second method. In Chapter II the stability and boundednessof solutions are discussed. Positive limiting sets and thesemi-invariant set are used to discuss the asymptotic behavior ofsolutions (an extension of stability theory) in Chapter III. Then,in Chapter IV extreme stability and stability of a set are discussedwhere sufficient conditions are established. In Chapter V conversetheorems on stability and boundedness are discussed and utilizedin Chapter VI to derive properties of solutions of perturbed systemsand the asymptotic behavior of solutions near integral manifolds.Next, using fixed point theorems and Liapunov functions,existence of periodic and almost periodic solutions is discussed inChapter VII. The concluding Chapter VIII shows hOw Liapunov'ssecond method may be generalized to functional-differential equationsto obtain similar results to those for ordinary differentialequations.