Estimation of reachable set for switched singular systems with time-varying delay and state jump

This paper addresses the estimation problem of the reachable set for switched singular systems with state jump under initial condition and bounded peak disturbance. The aim is to determine a bounded set that contains all reachable states. Initially, a state jump lemma is presented for switched singular systems. Then, a new bounding lemma is shown by analyzing the variation of piecewise continuous functional in subintervals and referencing the definition of the average dwell-time. Afterwards, using lemmas and linear matrix inequalities, sufficient conditions are derived for switched singular systems with and without time-varying delay, which ensure that the state trajectory of the system remains within a closed bounded set. Finally, the obtained results are validated through numerical examples.