A quadratic stability result for singular switched systems with application to anti-windup control

In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A-gh
^T
, and where one of the matrices is singular. We then apply this result in a study of a feedback system with a saturating actuator.