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Stability conditions of pulse-width-modulated systems through the second method of Lyapunov

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2 Author(s)
Kadota, T. ; Bell Telephone Laboratories, Inc., Whippany, NJ, USA ; Bourne, H.C.

PWM systems contain inherent nonlinearities which arise from their modulation scheme. Thus, for a legitimate study of stability, such systems must be treated as nonlinear sampled-data systems without initially resorting to linear approximations. For a nonlinear system whose dynamic behavior is described by a set of first-order difference equations, one of the theorems in the second method of Lyapunov gives, as a sufficient condition for asymptotic stability in the large, the existence in the whole space of a positive-definite Lyapunov's functionV, whose differenceDeltaVis negative definite. Hence, by choosing a positive-definite quadratic form asV, the sufficient condition is reduced to the negative-definiteness in the whole space ofDeltaV. Upon this basis, a systematic procedure of obtaining analytically a sufficient condition for asymptotic stability in the large is developed for various types of PWM systems; the condition is stated as the negativeness of all the eigenvalues of three matrices associated with the PWM system.

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Automatic Control, IRE Transactions on  (Volume:6 ,  Issue: 3 )