Abstract
In this article a novel robust controller for the control of switched nonlinear systems with asynchronous switching is proposed considering state delays. The proposed approach improves the actual methodologies found in literature in which the disturbance rejection properties of these two methodologies consider a disturbance equal to zero but the proposed robust controller considers any kind of disturbances that makes this strategy to surpass other similar methodologies. The main objective is that the robust controller stabilizes the studied system in matched and unmatched modes considering the dwell time in order to obtain an exponentially stable closed loop system. Another characteristic of the proposed control strategy is that a conmutative control law in both matched and unmatched cases is designed with a linear part, where the gain matrices for the linear part are obtained by linear matrix inequalities LMI's along with a nonlinear controller part.