A further result on attainable states for a class of nonlinear systems with constraints

We consider a class of nonlinear systems where the control and state variables are submitted to explicit constraints. Let A_T denote the set of all attainable states from the origin at time T, while observing state and control constraints along the whole trajectory. One of our previous main results (1994) gives an estimation of A_T as a ball of the state space Rⁿ, with a computable radius. The approach makes use of the contraction mapping theorem. Hence, the estimation thus obtained may be rather conservative in some applications. This paper is an attempt to get a better estimation of the set A_T by using other topological devices. The main one is an extended version of the continuation principle, obtained by Mawhin (1993)