دانلود کتاب Stability Theory by Liapunov's Second Method

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In this monograph, I shall discuss the stability and boundedness of solutions of differential equations and related topics; the underlying theme and connective thread being Liapunov's second method. I have attempted to give an introduction to Liapunov's second method which incorporates recent modifications and illustrates the scope and power of this method. There is a vast literature on the theory and applications of Liapunov's second method, and due to the nature of this series and the resultant restrictions in size, I have emphasized the derivation and application of stability criteria for ordinary differential equations. As in any monograph of this nature, the selection of topics has also been dictated by the interests of the author. Liapunov's second method is also an important tool in the theory of control systems, dynamical systems and functional-differential equations. Since an excellent book on stability theory in control systems has been published recently by Lefschetz [79], I have omitted all statements on control systems. For the stability in control systems, see [72], [74], [78]-[80], [153]. For dynamical systems, there are many interesting investigations [8]-[10], [15], [76], [103], [152], but dynamical systems are briefly treated in Section 22. Functional-differential equations are considered in Chapter VIII where a Liapunov function is generalized to a Liapunov functional 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 one by 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 introduces Liapunov's second method. In Chapter II the stability and boundedness of solutions are discussed. Positive limiting sets and the semi-invariant set are used to discuss the asymptotic behavior of solutions (an extension of stability theory) in Chapter III. Then, in Chapter IV extreme stability and stability of a set are discussed where sufficient conditions are established. In Chapter V converse theorems on stability and boundedness are discussed and utilized in Chapter VI to derive properties of solutions of perturbed systems and 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 in Chapter VII. The concluding Chapter VIII shows hOw Liapunov's second method may be generalized to functional-differential equations to obtain similar results to those for ordinary differential equations.