Controllability of nonlinear systems consisting of a bilinear mode with distributed delays in control. (English) Zbl 0542.93008

Somasundaram, D.; Balachandran, K.

IEEE Trans. Autom. Control 29, 573-575 (1984).

Relative global controllability of nonlinear, nonstationary dynamical systems consisting of a bilinear mode with distributed delays in control is considered. Using Schauder’s fixed point theorem sufficient conditions for global relative controllability are given. The presented results are a straightforward generalization of the results given in the papers of J. Klamka [Int. J. Control 31, 811-819 (1980; Zbl 0462.93009)] and K. C. Wei and A. E. Pearson [IEEE Trans. Automatic Control AC-23, 486-488 (1978; Zbl 0397.93005)]. Bilinear systems with multiple lumped delays in the control and general nonlinear dynamical systems are also considered in the paper, and appropriate controllability criteria are presented without proofs. Moreover, a simple illustrative numerical example is given.

Reviewer: J.Klamka

MSC:

93B05	Controllability
47H10	Fixed-point theorems
93C10	Nonlinear systems in control theory
34K35	Control problems for functional-differential equations
93C15	Control/observation systems governed by ordinary differential equations
93C99	Model systems in control theory

Keywords:

Relative global controllability; distributed delays in control; Schauder’s fixed point theorem; Bilinear systems

Citations:

Zbl 0462.93009; Zbl 0397.93005