Abstract
SUMMARYThis paper addresses the problem of determining the stability margin Ms in linear time‐invariant electric circuits whose parameters R, L, C, M and controlled source coefficients α are allowed to take on fixed but unknown values within corresponding preset intervals. A method for solving the above robust stability problem is suggested. Unlike previous results resorting to the state–space formulation, the new method is based on an appropriate description of the circuit considered using a specific model in semi‐state form. The set of differential algebraic equations (DAEs) thus obtained contain the circuit parameters in a linear manner. The latter property permits Ms to be determined in an efficient way using the right endpoint of the range related to the real part of the first (closest to the imaginary axis) eigenvalue of a corresponding interval generalized eigenvalue problem. The new method is shown to have polynomial numerical complexity with respect to the size of the generalized eigenvalue problem. Two numerical examples illustrating the new DAE approach are provided. Copyright © 2011 John Wiley & Sons, Ltd.
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