Controllability of a class of perturbed nonlinear systems. (English) Zbl 0637.93011

Sufficient conditions are established for the controllability of general nonlinear systems of the form \(\dot x=g(t,x)+B(t,x)u+f(t,x,\dot x,u)\).


93B05 Controllability
93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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[1] V. M. Alekseev: An estimate for the perturbations of the solutions of ordinary differential equations. Vestnik Moskov. Univ. Ser. I. Mat. Meh. (1962), 2, 28-36. In Russian.
[2] K. Balachandran: Global and local controllability of nonlinear systems. Proc. IEE – Part D, Control Theory and Applications 132 (1985), 1, 14-17. · Zbl 0554.93012
[3] K. Balachandran, J. P. Dauer: Controllability of nonlinear systems via fixed point theorems. J. Optim. Theory Appl. 53 (1987), 3, 345-352. · Zbl 0596.93010
[4] K. Balachandran, D. Somasundaram: Controllability of a class of nonlinear systems with distributed delays in control. Kybernetika 19 (1983), 6, 475-482. · Zbl 0528.93012
[5] C. Dacka: On the controllability of a class of nonlinear systems. IEEE Trans. Automat. Control AC-25 (1980), 2, 263-266. · Zbl 0439.93006
[6] J. P. Dauer: Nonlinear perturbations of quasi-linear control systems. J. Math. Anal. Appl. 54 (1976), 3, 717-725. · Zbl 0339.93004
[7] J. P. Dauer: Controllability of perturbed nonlinear systems. Atti Acad. Naz. Lincei: Rendiconti 63 (1977), 5, 345-350. · Zbl 0413.93012
[8] L. E. May: Perturbations in fully nonlinear systems. SIAM J. Math. Anal. 1 (1970), 3, 376-391. · Zbl 0204.40302
[9] B. G. Pachpatte: Stability and asymptotic behaviour of perturbed nonlinear systems. J. Differential Equations 16 (1974), 1, 14-25. · Zbl 0298.34045
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