Interval exponential input-to-state stability for switching impulsive systems with application to hybrid control for micro-grids

This paper studies the interval exponential input-to-state stability (interval e-ISS) for switching impulsive systems (SIS). The notions of interval e-ISS and interval event-e-ISS are defined for SIS. And the SIS are classified into the time-based SIS and the state-based SIS according to whether the switching control is driven by time or state. By using the decomposition of the interval matrix and the method of variation of constants formula, the equivalence between interval e-ISS and e-ISS is established for the time-based SIS. It shows the time-based SIS has interval e-ISS if and only if its average-value system has e-ISS. And the criteria of interval e-ISS and interval event-e-ISS for the time-based SIS and the state-based SIS are derived separatively. Then, the result is used to test the ISS property for a micro-grid under hybrid control. The simulations for the micro-grid have been worked out to illustrate the results.