The state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:
(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;
(2) a control function u(t) is constructed such that
a) u(t) satisfies constrained energy or amplitude condition,
b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,
c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].