Titlebook: Introduction to the Theory of Stability; David R. Merkin Textbook 1997 Springer-Verlag New York, Inc. 1997 Approximation.calculus.differen

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The Frequency Method of Stability Analysis,quency characteristic is invariant in nonsingular linear coordinate transformations, and it may be obtained in a simple manner either from system equations or experimentally. Moreover, this method is applicable to a wider class of systems.

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Textbook 1997th each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that ex

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Introduction,of a system will be stable are not always as clear. The criterion for stability of rigid bodies in equilibrium under gravitational forces was formulated by E. Torricelli in 1644. In 1788, G. Lagrange proved a theorem that defines sufficient conditions for stability of equilibrium of any conservative system (see Section 3.1).

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Stability in First Approximation, this problem can be formulated in the following way:Equations of a perturbed motion are given as.where the nonlinear terms ., ..., . are terms of order higher than one in ., ..., . (in this chapter we will write just . instead of .).

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Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems,cording to a given law. All deviations from the desired conditions that may arise in the control system must be reduced to zero with time. In other words, the control system must be asymptotically stable.

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Introduction,w that some equilibrium states of a system are stable with respect to small perturbations, whereas other balanced states, although available in principal, cannot be realized in practice. Thus, for instance, when a pendulum is in its lowest position any small perturbations will result only in its osc

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Formulation of the Problem,nates, velocities, currents, voltages, temperatures, etc., or functions of these parameters. It is assumed that the number of variables .,?,. is finite and the system’s motion, i.e., the process of the changing of .,?, .. in time, is described by ordinary differential equations resolved with respect

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The Effect of Force Type on Stability of Motion,e possible effects of various physical factors on stability of motion. Meanwhile, in many cases such an analysis, in a rather general sense, may be very useful. In this chapter we present the effect of various types of forces on stability of motion.