Synthesis of Switched Linear Systems handling Sliding Motions

The synthesis problem on how to select the linear vector fields among the possible ones such that a switched system becomes (exponentially) stable is treated in this paper. Earlier synthesis results guarantee stability under the restriction that sliding motions do not occur. In this paper, we extend the design procedure allowing sliding motions to occur by introducing additional conditions. Furthermore, if desirable sliding motions can be avoided by introducing hysteresis in the switching strategy. One example is given to illustrate the synthesis procedure