On Stability of Switched Differential Algebraic Equations: A Decomposition-Based Approach

In this letter, we prove a Lie algebraic decomposition (of a certain Lie algebra, associated with the system, into a direct sum of its radical and a compact Lie algebra) based criterion for the stability of switched differential algebraic equations (DAEs). The Lie algebraic criterion guarantees exponential stability for the class of all switching signals, where the infimum of the switching durations associated with a switching signal is non-zero. We then show that this result generalizes the existing Lie algebraic solvability based stability criteria for switched DAEs.