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A simple and elementary proof of the non-conservativity theorem of Fang, Lin and Rotea

A simple and elementary proof of the non-conservativity theorem (i.e. Theorem 3 in Fanget al. [2008, On integral quadratic constraints approach to the analysis and design of linear systems subject to actuator saturation.Syst. Control Lett. , 57, 611–619.]) is given, which is related to the characterization of a contractively invariant ellipsoid for a class of linear systems under actuator saturation. Moreover, two slips of the pen, appearing in the process of transforming the optimization estimation problem of the domain of attraction into a linear matrix inequality optimization problem in the paper mentioned above, are revised.