LMIs in Control/Stability Analysis/Stability under Arbitrary Switching

The System

\begin{matrix} \dot{x} (t) \in {A_{1} x (t), A_{2} x (t)} \end{matrix}

The matrices $A_{1}, A_{2}$ .

\begin{matrix} Find & P > 0 : \\ A_{1}^{T} P + P A_{1} < 0 and \\ A_{2}^{T} P + P A_{2} < 0 \end{matrix}

The switched system is stable under arbitrary switching if there exists some P > 0 such that the LMIs hold.

LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.