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**Controllability of nonlinear systems with delays in both state and control variables.**
*(English)*
Zbl 0605.93009

Relative controllability of nonlinear systems with distributed delays in state and control is considered. Using the Schauder fixed point theorem, sufficient conditions for relative controllability are obtained. These conditions extend some previous results by considering a more general class of dynamical systems.

### MSC:

93B05 | Controllability |

34K35 | Control problems for functional-differential equations |

93C10 | Nonlinear systems in control theory |

47H10 | Fixed-point theorems |

93B03 | Attainable sets, reachability |

### Keywords:

Relative controllability; nonlinear systems with distributed delays; Schauder fixed point theorem
Full Text:
EuDML

### References:

[1] | H. T. Banks: Representations for solutions of linear functional differential equations. J. Differential Equations 5 (1969), 2, 399-409. · Zbl 0165.42701 |

[2] | D. H. Chyung: Controllability of linear time-varying systems with delays. IEEE Trans. Automat. Control AC-16 (1971), 5, 493-495. |

[3] | S. V. Curakova: The relative controllability of linear systems with variable and distributed retardation. Differencial’nye Uravnenija 5 (1969), 6, 1068- 1075. |

[4] | D. H. Chyung, E. B. Lee: Delayed action control problems. Automatica 6 (1970), 3, 395-400. · Zbl 0203.47001 |

[5] | J. P. Dauer: Nonlinear perturbations of quasi-linear control systems. J. Math. Anal. Appl. 54 (1976), 3, 717-725. · Zbl 0339.93004 |

[6] | J. P. Dauer, R. D. Gahl: Controllability of nonlinear delay systems. J. Optim. Theory Appl. 21 (1977), 1, 59-70. · Zbl 0325.93007 |

[7] | J. Klamka: On the controllability of linear systems with delays in the control. Internat. J. Control 25 (1977), 6, 875-883. · Zbl 0361.93012 |

[8] | J. Klamka: Relative controllability of nonlinear systems with distributed delays in control. Internat. J. Control 28 (1978), 2, 307-312. · Zbl 0402.93012 |

[9] | A. Manitius: On the controllability conditions for systems with distributed delays in state and control. Arch. Automat. Telemech. 17 (1972), 4, 363-377. · Zbl 0246.93006 |

[10] | A. Manitius, A. W. Olbrot: Controllability conditions for systems with delayed state and control. Arch. Automat. Telemech. 17 (1972), 2, 119-131. · Zbl 0237.93007 |

[11] | D. Somasundaram, K. Balachandran: Controllability of nonlinear systems consisting of a bilinear mode with distributed delays in control. IEEE Trans. Automat. Control AC-29 (1984), 6, 573-575. · Zbl 0542.93008 |

[12] | K. Balachandran: Controllability of nonlinear perturbations of linear systems with distributed delays in control. Robotica 3 (1985), 2, 89-91. |

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