Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability (ISS) problem for impulsive switched singular systems (ISSSs) with mismatched disturbances. In this paper, 'disturbance' is a general concept that includes model uncertainty, unknown system dynamic, external disturbance, etc. The modified uncertainty and disturbance estimator (UDE)-based control method is presented for singular systems and ISSSs, a virtual control is introduced to offset the effects of mismatched disturbances. On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time (AED-ADT) method, several sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure that the closed-loop systems are regular, impulse-free and ISS. Finally, two examples are given to demonstrate the effectiveness of the proposed results.