Abstract
One of the noticeable aspects of the theory of dynamics is the prevalence, since the work of Lyapunov and Poincaré, of first order differential equations. Of course, there are good conceptual and theoretical reasons for this, connected with the notion of state and the specification of initial conditions. Since the late fifties also areas as control theory have relented to this point of view. This introduction of state models in fact brought with it a renaissance in this field.
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References
J.C. Willems and H.L. Trentelman, On quadratic differential forms, SIAM Journal on Control and Optimization, to appear.
J.C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions on Automatic Control, volume 36, pages 259–294, 1991.
D. Cox, J. Little, and D. O’Shea, Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd edition, Springer Verlag, 1997.
M. Fliess, Automatique et corps différentiels, Forum Mathematicae, pages 227–238, 1989.
M. Fliess and S.T. Glad, An algebraic approach to linear and nonlinear control, pages 223–267 of Essays on Control: Perspectives in the Theory and Its Applications, edited by H.L. Trentelman and J.C. Willems, Birkhäuser, 1993.
E.D. Sontag, Polynomial Response Maps, Springer-Verlag, 1979.
Y. Wang and E.D. Sontag, Algebraic differential equations and rational control systems, SIAM Journal on Control and Optimization, volume 30, pages 1126–1149, 1992.
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© 1999 Springer-Verlag London Limited
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Willems, J.C. (1999). Lyapunov theory for high order differential systems. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_50
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_50
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