Switching rule design for affine switched systems using a max-type composition rule

This paper presents conditions for designing a switching rule that drives the state of the switched dynamic system to a desired equilibrium point. The proposed method deals with the class of switched systems where each subsystem has an affine vector field and considers a switching rule using ‘maxmax’ composition. The results guarantee global asymptotic stability of the tracking error dynamics even if sliding mode occurs at any switching surface of the system. In addition, the method does not require a Hurwitz convex combination of the dynamic matrices of the subsystems. Two numerical examples are used to illustrate the results.