Stabilizability of Switched Differential Algebraic Equations: A Solvability-Based Approach

In this letter, we establish a Lie algebraic solvability-based criterion for stabilizability of switched differential algebraic equations (switched DAEs) consisting of individually unstable subsystems. It is well known that the Lie algebra generated by commuting matrices is trivially solvable. Thus, the Lie algebraic stabilizability criterion of this letter generalizes the existing commutativity-based criterion in the literature. Furthermore, for switched DAEs satisfying the Lie algebraic criterion, we explicitly provide a simple method to construct a stabilizing switching signal and demonstrate the same with the help of an example.