Stability of delayed switched systems involving impulses: State-dependent switching control approach

This paper mainly considers the exponential stability problem for delayed switched systems involving impulses via state-dependent switching (SDS) approach, where both stabilizing and destabilizing impulses are considered. Different from traditional SDS method in the framework of continuous state space, we propose an SDS law depending on time delays under impulse environment. Based on the designed SDS strategy, some sufficient conditions are provided to guarantee the global exponential stability (GES) of the system. It shows that in the coexistence environment of impulses and time delays, the stability of the system can still be achieved via the SDS law even if all the modes are unstable. Finally, we present two simulation examples to illustrate the feasibility and validity of our main results.