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Each is open and dense in R . (37) is a homeomorphism between U an open and dense subset Θ of R , with d = n(p + s ) : Θ S(i) = Ü if and = Φ (U ) . |μ| = n. Since U , |μ| = n, is open and dense in S ( n ) , it follows that almost all points of S(n) are in U μ. We for any such The choice of a partition μ specifies a local coordinate system. Therefore, once n is chosen, a system in S(n) can be described in almost any coordinate system such that |μ| = n. We shall see later that the partition μ and the corresponding coordinate vector τ ARMAX) form.

NEHORAI and M. MORF, "Recursive Identification Algorithms for Right Matrix Fraction Description Models," IEEE Trans. Autom. Control AC-29, 1103-1106 (1984). 18. C. T. CHEN, "Adaptive Control of Linear Multivariable Sys­ tems without any Prior Knowledge," Proo. IEEE Conf. Deci­ sion Control, 1882-1887 (1985). 19. J. J. DONGARRA, C. B. MOLER, J. R. BUNCH, and G. W. STEWART, "LINPACK User's Guide," SIAM, Philadelphia, Pennsylvania, 1979. Control and Dynamic Systems Techniques for the Selection of Identifiable Parametrizations for Multivariable Linear Systems MICHEL GEVERS VINCENT WERTZ Laboratoire d'Automatique, de Dynamique et d Analyse des Systdmes Louvain University B-1348 Louvain la Neuve, Belqium I.

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