A unified eigenvalue theory for time-varying linear circuits and systems

Linear time-varying circuits and systems of the vector form dx/dt=A(t)x+bu and the scalar form y/sup (n)/+ alpha /sub n/(t)y/sup (n-1)/+ . . . + alpha /sub 2/(t)dy/dt+ alpha /sub 1/(t)y=u can be studied as operators over a differential ring K of almost everywhere C/sup infinity / functions. A unified (time-varying) eigenvalue theory has been recently developed for such operators, relative to a class of equivalence transformations on K/sup n*n/. This unified eigenvalue theory leads to the natural time-varying counterparts of eigenvalues, eigenvectors, characteristics, equations, modal matrices, stability criteria, etc., as traditionally used for time-invariant linear circuits and systems. The main results of the theory are summarized. The time-varying counterparts of transfer functions, series/parallel realizations, and pole-assignment control technique for the scalar form are presented.<<ETX>>

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