New Concepts for the Generalized Eigenvalue Problem with Applications to Dynamical Systems with Perturbed Coefficients

Abstract eng:
In this paper we study the generalized eigenvalue problem Ax=λBx for matrices with II-order perturbations with use of perturbation numbers. Such general formulation appears in many engineering applications. For example, many of coefficients of technical systems are known with some tolerance only. The dynamic system behaviour is thus best described by equations incorporating perturbed matrices. Designing robust stabilisation systems under these conditions becomes a problem of a great practical importance. Thus the stability analysis of perturbed dynamical systems reduces to the analysis of the properties of a real or complex matrices. Applications to dynamical systems described by second-order differential equations with perturbed coefficients are presented. The results improve considerably the earlier results of Skrzypczyk.

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