Abstract
This chapter discusses the Mikhailov's stability criterion, the algebraic stability criteria, the frequency stability criterion, and the width of stability region and stability reserve. Mikhailov's stability criterion for the linear automatic regulation systems (and other dynamic systems) of arbitrary order was proposed by Aleksandr Vasil’evich Mikhailov in 1936. It follows directly from the properties of the Mikhailov curve. The chapter discusses what forms may be taken on by the Mikhailov curve for stable and unstable systems. The founder of the theory of automatic regulation I. A. Vyshnegradskii in investigating a given third-order automatic regulation system, in 1876, proposed a stability criterion having general value for arbitrary dynamic systems described by the ordinary third-order linear differential equations. The characteristic equation of the third-order system will be a0z3 + a1z2 + a2z + a2, = 0. The chapter discusses Vyshnegradskii's hyperbola and parameters and contradiction between static precision and dynamic stability.
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