Computation of minimal-order state-space realizations and observability indices using orthogonal transformations

In this paper, an algorithm is presented for obtaining a minimal-order state-space realization of a strictly proper rational function matrix. The algorithm can also be used to compute the observability indices of any given state-space system. A controllable but unobservable state-space realization of the given rational function matrix is first obtained, by inspection. The algorithm then performs a sequence of simple coordinate transformations on the state vector of the system. The coordinate transformation matrices are orthogonal and are easily constructed from the system matrices. Each coordinate transformation operates on submatrices (of the state-space system matrices) of lower dimension than the preceding one. The sequence of coordinate transformations terminates after at most v 1 + 1 transformations, where v 1, is the maximal observability index of the state-space model. The observability indices of the system are also determined at this time. The transformed system matrices are obtained in a form wh...

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