Global and local controllability of nonlinear systems. (English) Zbl 0554.93012

Balachandran, K.

IEE Proc., Part D 132, 14-17 (1985).

Sufficient conditions are established for the global and local controllability of nonlinear systems of the form \(\dot x(\)t)\(=A(t,x(t),\dot x(t))x(t)+B(t,x(t),\dot x(t))u(t)+f(t,x(t),\dot x(t),u(t))\). The results are obtained using the measure of noncompactness of a set and Darbo’s fixed point theorem.

MSC:

93B05	Controllability
47H10	Fixed-point theorems
93C10	Nonlinear systems in control theory
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

global and local controllability; measure of noncompactness; Darbo’s fixed point theorem