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Topological classification and structural stability of linear systems. (English) Zbl 0394.93024


MSC:

93B99 Controllability, observability, and system structure
93C05 Linear systems in control theory
93B05 Controllability
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
93C99 Model systems in control theory
93D99 Stability of control systems

Citations:

Zbl 0251.58008
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References:

[1] Kuiper, N. H.: The topology of the solutions of a linear differential equation on rn. Proceedings of the international conference on manifolds and related topics in topology, 195-203 (1975)
[2] Wonham, W. M.: Linear multivariable control, A geometric approach. Lecture notes in economics, no. 101 (1974) · Zbl 0314.93007
[3] Arnold, V. I.: Ordinary differential equations. (1973) · Zbl 0296.34001
[4] Ladis, N. N.: Topological-equivalence of linear flows. Differencial’nye uravnenija 9, 1222-1235 (1973)
[5] Hermann, R.; Martin, C.: Algebro-geometric and Lie-theoretic techniques in systems theory. Interdisciplinary mathematics (1977) · Zbl 0362.93002
[6] Rosenbrock, H. H.: State-space and multivariable theory. (1970) · Zbl 0246.93010
[7] Brunovský, P.: A classification of linear controllable systems. Kybernetika (Prague) 3, 173-187 (1970) · Zbl 0199.48202
[8] Kalman, R. E.: Kronecker invariants and feedback. Ordinary differential equations, 459-471 (1972) · Zbl 0308.93008
[9] Hirsch, M. W.; Smale, S.: Differential equations, dynamical systems, and linear algebra. (1974) · Zbl 0309.34001
[10] Martin, C.; Hermann, R.: Applications of algebraic geometry to systems theory: the mcmillan degree and Kronecker indices of transfer functions as topological and holomorphic system invariants. SIAM J. Control optimization 16, 743-755 (1978) · Zbl 0401.93020
[11] Kuiper, N. H.; Robbin, J. W.: Topological classification of linear endomorphisms. Invent. math. 19, 83-106 (1973) · Zbl 0251.58008
[12] Bhockett, R. W.: Feedback invariants for nonlinear systems. Preprints of the 7th triennial IFAC world congress 1, 1115-1120 (1978)
[13] Heymann, M.: Controllability subspaces and feedback simulation. SIAM J. Control optimization 14, 769-789 (1976) · Zbl 0354.93026
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