Stabilization to ISS for Discrete-time Impulsive Hybrid Systems with Mixed K -Dissipativity

Abstract

This paper studies the stabilization to ISS (input-to-state stability) issue for discrete-time impulsive hybrid systems (DIHS) with mixed K -dissipativity property. Firstly, the new concept of mixed K -dissipativity is proposed for DIHS. Then, the criteria of stabilization in the sense of ISS are derived for mixed K -dissipative DIHS. It shows that for a mixed K -dissipative DIHS, under the same state feedback control, even if all subsystems have no ISS, the whole DIHS may still has ISS property. The results are then used to study the case of network via impulsive interconnections. The linear matrix inequality (LMI) conditions for K -dissipativity of every DIHS in the network under the mixed quadratic supply rate are derived. Moreover, the interconnection control is designed to stabilize the network to ISS. Finally, one example is given for illustration.