Quadratic Stability Margin in Switched Control System Design

While a quadratic common Lyapunov function (QCLF) is not necessary for a switched system to be stable, a system which admits a QCLF has an exponential stability guarantee that can be particularly useful in satisfying control system design requirements. A natural direction of inquiry is to quantify the fragility or robustness of the exponential stability guarantee with respect to uncertainty in the switched system. This work develops an approximation of the quadratic stability margin in the form of bounded perturbations to the system dynamics, providing a robustness description directly comparable to parameterized system uncertainty.