Simple Topics in Stability Theory
This chapter is varied in character. It is meant to complete the elementary view of stability theory which we began to present in Chapter I. Sections 1 and 2 examine in different ways what conclusions can be drawn from the knowledge of a positive definite auxiliary function V(t,x) possessing a derivative which is only smaller than or equal to zero. Section 3 is an elementary presentation of the so-called comparison method. All these matters will be investigated further in later chapters. Section 4 deals briefly with total stability, i.e. stability with respect to perturbations not only of the initial conditions, but also of the second member of the differential equation. The main theorem proved here will be needed in Chapter IV. Section 5 is but a glance at the “frequency method”, introduced here because of its intrinsic importance and for the sake of completeness, but considered later as outside the scope of the rest of the book.
KeywordsAsymptotic Stability Stability Theory Auxiliary Function Global Asymptotic Stability Frequency Method
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