Abstract
The QZ algorithm gives a robust way of computing solutions to the generalized eigenvalue problem. The generalized eigenvalue problem is used in linear control theory to find solutions to Ricatti equations, as well as to determine system transmission zeros. In state-space linear system analysis, the system poles and transmission zeros are particularly important for determining system time and frequency response. Here, we embed calculation of the eigenvalue derivatives in the QZ algorithm such that the derivatives of system poles and transmission zeros are computed simultaneously with the poles and zeros themselves. The resulting method is further exercised in finding generalized eigenvalues and their sensitivities required for finding the derivatives of system residues. This technique should open the door to solutions of problems of interest by unconstrained gradient-based methods. Typical numerical results are presented.
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