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Null controllability of nonlinear infinite neutral systems with delays in control. (English) Zbl 0933.93014

Nonlinear, continuous-time neutral control systems with infinite distributed delays in the state variables and multiple time-varying lumped delays in the control are considered. Using Schauder’s fixed-point theorem, a sufficient condition for global relative null controllability in a given time interval is formulated and proved. In the proof, the unsymmetric Fubini theorem and the Riesz theorem are used. Moreover, several remarks and comments on controllability problems for control systems with different types of delays are also given. Relations to results existing in the literature are presented. The sufficient condition for null controllability given in the paper extends, for more general control systems with delays, the results presented in the papers [J. Klamka, Int. J. Control 24, 869-878 (1976; Zbl 0342.93006); ibid. 31, 811-819 (1980; Zbl 0462.93009)].

MSC:

93B05 Controllability
93C23 Control/observation systems governed by functional-differential equations
93C10 Nonlinear systems in control theory
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