Abstract
The stability of distributed- parameter systems described by linear partial differential equations is investigated by reducing the original equations by a change of variables to a system of first-order equations in time and in spatial coordinates. The Lyapunov functions are constructed in the form of single integral forms. New necessary and sufficient conditions for the sign-definiteness of these forms are obtained. These conditions, unlike the Sylvester criterion, do not require the calculation of determinants. The check for sign-definiteness is made using recurrence relationships and is a generalization of the results obtained in /1/. The proposed criteria are applied to derive sufficient conditions for the stability of distributed-parameter linear systems. The construction of functionals for the one-dimensional second-order linear hyperbolic equation is considered in more detail. As an example, we examine the stability of the torsional oscillations of an aircraft wing.
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