A Necessary and Sufficient Condition for Stability of Arbitrarily Switched Second-Order LTI System: Marginally Stable Case

In this paper, the stability analysis for a class of second order switched LTI systems with possible marginally stable subsystems is investigated. The main contribution here is the derivation of a necessary and sufficient condition for stability of such a switched system under arbitrary switching. The condition can be easily checked which is illustrated by an example.