Concerns linear parametrically varying systems (LPVs) with brief instabilities. LPVs provide a framework for the study of nonlinear systems, by analyzing related linear time-invariant systems parameterized by a parameter p that lives in a compact set. This paper presents tools for stability and performance analysis of LPVs with brief instabilities, where performance is evaluated in terms of L/sub 2/ induced norms. The main results show that stability and performance can be assessed by examining the feasibility of parameterized sets of linear matrix inequalities (LMI). An application to the problem of designing a nonlinear vision/inertial navigation filter for an aircraft approaching an aircraft carrier is included. The results developed provide the proper framework to deal with out-of-frame events that arise when the vision system loses its target temporarily. Field tests with a prototype unmanned air vehicle illustrate the performance of the filter and illustrate the scope of applications of the new theory developed.