Optimal switched law for the linear impulsive switched systems based on norm

Optimal switched law, which is for the linear impulsive switched system, is discussed in this paper. First, we show that if the constraint condition of the matrix pencil is satisfied, we could obtain the asymptotically stable range of the linear impulsive switched system. For a stable linear impulsive switched system, different switched laws determine different convergence process. Then the method of the optimal switched law based on norm is studied. Finally, a simulation example is given to illustrate the correctness of our conclusions presented.