Abstract
Interest in bilinear systems theory and applications has grown in the recent years. The basic motivation of this growth is twofold: on the one hand, the feasibility to be a satisfactory model for large classes of systems (physical, biological, socio-economical, etc.); on the other hand the relative ease with which their theory can be set-up. The first characteristic is substantially related to the presence of a multiplicative control action (on the state motion) besides the additive one, which is the only one present in a linear system. The second characteristic lies in the fact that, for any fixed input, the equations are linear in the state.
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References
R.R.MOHLER, Bilinear control processes with applications to engineering, ecology and medicine, Academic Press, New York (1973).
C.BRUNI, G.DI PILLO, G.KOCH, Bilinear systems: an appealing class of “nearly linear” systems in theory and applications. IEEE Trans. Automatic Control, AC 19 (1974), to appear.
P.d’ALESSANDRO, A.ISIDORI, R.RUBERTI, Realization and structure theory of bilinear dynamical systems, SIAM J. Control, 12 (1974), to appear.
P.d’ALESSANDRO, A.ISIDORI, R.RUBERTI, Lectures an Bilinear System Theory, Notes for a Course held at C.I.S.M., Udine (Italy), Springer Verlag (Wien), 1972.
R.W.BROCKETT, On the algebraic structure of bilinear systems, Theory and Applications of Variable Structure Systems (R.R. Mohler and A. Ruberti, eds.), Academic Press, New York (1972), pp. 153–168.
A.ISIDORI, Direct construction of minimal bilinear realizations from nonlinear input/output maps, IEEE Trans. Automatic Control, AC 18 (1973), to appear.
A.ISIDORI, The computation of reduced forms for bilinear systems, Ricerche di Automatica, 3 (1972), pp. 296–299.
C.BRUNI, G.DI PILLO, G.KOCH, On the mathematical models of bilinear systems, Ricerche di Automatica, 2 (1971), pp. 11–26.
R.E.KALMAN, P.L.FALB, M.A.ARBIB, Topics in mathematical system Theory, Mc Graw Hill (New York), 1969, pp. 288–308.
A.J.TETHER, Construction of linear state-variable models from finite input/output data, IEEE Trans. Automatic Control, AC 15 (1970), pp. 427–436.
H.H.ROSENBROCK, Computation of minimal representation of rational transfer function matrix, Proc. IEE, 115 (1968), pp. 325–7.
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© 1973 D. Reidel Publishing Company, Dordrecht
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Isidori, A., Ruberti, A. (1973). Realization Theory of Bilinear Systems. In: Mayne, D.Q., Brockett, R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2675-8_3
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DOI: https://doi.org/10.1007/978-94-010-2675-8_3
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