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Nonnegative realizations of matrix transfer functions. (English) Zbl 0989.93016

This paper is an important contribution to the theory concerning nonnegative realizability of matrix transfer functions.
The main result characterizes the nonnegative realizability of a scalar-valued transfer function with the help of primitive transfer functions and is extended to the general case of matrix-valued transfer functions.
In it there is also an algorithm for establishing whether a scalar-valued transfer function with nonnegative impulse function has a nonnegative realization.
The paper is clearly written, and its relation to the existing literature is clearly indicated.

MSC:

93B15 Realizations from input-output data
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[1] Anderson, B. D.O.; Deistler, M.; Farina, L.; Benvenuti, L., Nonnegative realization of a linear system with nonnegative impulse response, IEEE Trans. Circuits Systems - I: Fundamental Theory Appl., 43, 134-142 (1996)
[2] A. Berman, M. Neumann, R.J. Stern, Nonnegative Matrices in Dynamic Systems, Wiley, New York, 1989; A. Berman, M. Neumann, R.J. Stern, Nonnegative Matrices in Dynamic Systems, Wiley, New York, 1989 · Zbl 0723.93013
[3] A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979; A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979 · Zbl 0484.15016
[4] Burns, F.; Fiedler, M.; Haynsworth, E., Polyhedral cones and positive operators, Linear Algebra Appl., 8, 547-559 (1974) · Zbl 0299.15007
[5] Chen, C. T.; Desoer, C. A., Cotrollability and observability of composite systems, IEEE Trans. Automatic Control, AC-12, 402-409 (1967)
[6] Farina, L., On the existence of a positive realization, Sys. Control Lett., 28, 219-226 (1996) · Zbl 0866.93018
[7] Förster, K.-H.; Nagy, B., On nonnegative realizations of rational matrix functions and nonnegative input-output systems, Oper. Theory: Adv. Appl., 103, 89-104 (1998) · Zbl 0897.93017
[8] Förster, K.-H.; Nagy, B., Spectral properties of rational matrix functions with nonnegative realizations, Linear Algebra Appl., 275-276, 189-200 (1998) · Zbl 0934.15027
[9] F.R. Gantmacher, The Theory of Matrices, I-II., Chelsea, New York, 1966; F.R. Gantmacher, The Theory of Matrices, I-II., Chelsea, New York, 1966 · Zbl 0136.00410
[10] M. Gerstenhaber, Theory of convex polyhedral cones, Ch. XVIII in: T.C. Koopmans (Ed.), Activity Analysis of Production and Allocation, Wiley, New York, 1951, pp. 287-297; M. Gerstenhaber, Theory of convex polyhedral cones, Ch. XVIII in: T.C. Koopmans (Ed.), Activity Analysis of Production and Allocation, Wiley, New York, 1951, pp. 287-297
[11] I. Gohberg, P. Lancaster, L. Rodman, Invariant Subspaces of Matrices with Applications, Wiley, New York, 1986; I. Gohberg, P. Lancaster, L. Rodman, Invariant Subspaces of Matrices with Applications, Wiley, New York, 1986 · Zbl 0608.15004
[12] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966; T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966 · Zbl 0148.12601
[13] R.E. Kalman, Y.C. Ho, K.S. Narenda, Controllability of linear dynamical systems, in: Contributions to Differential Equations, Wiley, New York, 1961, p. 181; R.E. Kalman, Y.C. Ho, K.S. Narenda, Controllability of linear dynamical systems, in: Contributions to Differential Equations, Wiley, New York, 1961, p. 181
[14] H. Minc, Nonnegative Matrices, Wiley, New York, 1988; H. Minc, Nonnegative Matrices, Wiley, New York, 1988
[15] Ohta, Y.; Maeda, H.; Kodama, S., Reachability observability and realizability of continuous-time positive systems, SIAM J. Control Optimiz., 22, 171-180 (1984) · Zbl 0539.93005
[16] J.E. Rubio, The Theory of Linear Systems, Academic Press, New York, 1971; J.E. Rubio, The Theory of Linear Systems, Academic Press, New York, 1971 · Zbl 0227.93001
[17] Roitman, M.; Rubinstein, Z., On linear recursions with nonnegative coefficients, Linear Algebra Appl., 167, 151-155 (1992) · Zbl 0757.11005
[18] H.H. Schäfer, Banach Lattices and Positive Operators, Springer, New York, 1980; H.H. Schäfer, Banach Lattices and Positive Operators, Springer, New York, 1980
[19] H.H. Schäfer, Topological Vector Spaces, Springer, New York, 1971; H.H. Schäfer, Topological Vector Spaces, Springer, New York, 1971
[20] E.D. Sontag, Mathematical Control Theory, Springer, New York, 1990; E.D. Sontag, Mathematical Control Theory, Springer, New York, 1990 · Zbl 0703.93001
[21] Tam, B.-S.; Schneider, H., The core of a cone-preserving map, Trans. Amer. Math. Soc., 343, 479-524 (1994) · Zbl 0826.15015
[22] van den Hof, J. M., Realization of positive linear systems, Linear Algebra Appl., 256, 287-308 (1997) · Zbl 0871.93010
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