Minimal stable partial realization

An asymptotically stable minimal order realization of a partial sequence of Markov parameters is achieved by reducing the problem to a standard but minimal one in decision algebra. Summary—In this paper two equivalent sets of necessary and sufficient conditions for the existence of an asymptotically stable partial realization are developed. Both sets are expressed as multivariable polynomial equations which may be tested for the existence of a solution in a finite number of rational steps via decision methods. Should a solution exist, it may be evaluated with the aid of polynomial factorization. The first set of conditions are based on results due to Ho and Kalman, and are useful for the case where the number of specified Markov parameters is greater than the order of the realization. For other cases, the second set of conditions which include results from a companion paper on minimal observers, require less computational effort to be tested.