Nonlinear perturbations of quasilinear delay control systems. (English) Zbl 0661.93009

Sufficient conditions are established for controllability of nonlinear perturbations of quasilinear delay systems. These conditions are obtained by solving a system of nonlinear integral equations with the help of Schauder’s fixed point principle.


93B05 Controllability
34K35 Control problems for functional-differential equations
93C10 Nonlinear systems in control theory
47H10 Fixed-point theorems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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[1] K. Balachandran: Controllability of nonlinear perturbations of linear systems with distributed delays in control. Robotica 3 (1985), 2, 89-91.
[2] K. Balachandran: Controllability of nonlinear systems with delays in both state and control variables. Kybernetika 22 (1986), 4, 340-348. · Zbl 0605.93009
[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 · doi:10.1007/BF00938943
[4] K. Balachandran, J. P. Dauer: Controllability of perturbed nonlinear delay systems. IEEE Trans. Automat. Control AC-32 (1987), 2, 172-174. · Zbl 0614.93011 · doi:10.1109/TAC.1987.1104536
[5] J. P. Dauer: Nonlinear perturbations of quasi-linear control systems. J. Math. Anal. Appl. 54 (1976), 3, 717-725. · Zbl 0339.93004 · doi:10.1016/0022-247X(76)90191-8
[6] J. P. Dauer, R. D. Gahl: Controllability of nonlinear delay systems. J. Optim. Theory Appl. 21 (1977), 1, 59-70. · Zbl 0325.93007 · doi:10.1007/BF00932544
[7] R. D. Gahl: Controllability of nonlinear systems of neutral type. J. Math. Anal. Appl. 63 (1978), 1, 33-42. · Zbl 0406.34052 · doi:10.1016/0022-247X(78)90101-4
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