For a nonlinear/linear system the disturbance to which is restricted to a finite domain, the reachable domain in the state space from a given initial state is called a state reachable set. Though some theoretical approaches have been proposed on investigating state reachable sets, it is difficult to evaluate the state reachable set actually for general nonlinear systems by using these approaches directly.
In this paper, we introduce a quadratic system based on a quadratic approximation for nonlinear systems. Then we propose an approach based on linear matrix inequalities to investigate the reachable set of the quadratic system the disturbance to which is restricted to inside of a unit disc. In numerical case study, we demonstrate efficacy of the proposed approach by evaluating the state reachable set actually for a given quadratic system.