Mixed $\mathscr{K} $ -Dissipativity and Stabilization to ISS for Impulsive Hybrid Systems
Bin Liu, David John Hill, Zhijie Sun · IEEE Transactions on Circuits & Systems II Express Briefs · 2015
This brief studies the issue of dissipativity and related stabilization to input-to-state stability (ISS) for impulsive hybrid systems (IHSs). First, the concept of K-dissipativity is proposed. Then, the criteria of stabilization to ISS are derived for an IHS with K-dissipativity. It shows that, under the same state feedback control, although all subsystems have a nonnegative supply rate and thus have no ISS, the whole IHS may still have ISS. The results are then used to study the case of a network via impulsive interconnections. The linear matrix inequality conditions for the K-dissipativity of every node in the network under the quadratic supply rate are derived. Moreover, the interconnection control is designed to stabilize the network to ISS. Finally, one example is given for illustration.