Generalized Hankel Matrices and System Realization
Copyright policy )Generalized Hankel Matrices and System Realization
We define the Hankel matrix of an adjoint system. Adjoint systems include linear and bilinear systems, automata, and group systems in both the time-varying and time-invariant cases. Our definition of the Hankel matrix unifies the familiar $H_i^j = CA^{i + j} B$ of linear system theory (e.g. R. E. Kalman, P. L. Falb and M. A. Arbib, Topics in Mathematical Systems Theory, McGraw-Hill, New York, 1969) with the bilinear Hankel matrix of A. Isidori (Direct construction of minimal bilinear realizations from nonlinear input-output maps, IEEE Trans. Automatic Control, AC-18 (1973), pp. 626–631), T. J. Tarn and S. Nonoyama (Realization of discrete-time internally bilinear systems, Proc. IEEE Conf. Decision and Control, 76CH 1150-2CS (1976), pp. 125–133) and the Hankel matrix of M. Fliers (Matrices de Hankel, J. Math. Pure Appl., 53 (1974), pp. 197–224). The time-varying case is subsumed by regarding a time-varying system as a time-invariant system in a sequence category as in M. A. Arbib and E. G. Manes (Time-vary...
realization, adjoint system, automata, Canonical structure, Hankel matrix, Basic linear algebra, Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.), linear and bilinear systems, category theory, Algebraic theory of languages and automata, Linear systems in control theory, Realizations from input-output data, canonical and partial realizations
realization, adjoint system, automata, Canonical structure, Hankel matrix, Basic linear algebra, Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.), linear and bilinear systems, category theory, Algebraic theory of languages and automata, Linear systems in control theory, Realizations from input-output data, canonical and partial realizations
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