Combining L1 and L2 methods in the robust stability and performance analysis of nonlinear systems

In this paper, possible benefits of combining the two frameworks in the robust control are discussed. In particular, it is shown that the well-known absolute stability criterion by Zames-Falb (1968) for systems with monotonic nonlinearities (in particular, for systems with saturation) can be improved by using the magnitude bounds derived from the “L1” theory. In conjunction with this result, a lower bound of the Zames-Falb stability margin is derived, by using a duality approach. In the second part of the paper, it is shown how the analysis of the worst case output error magnitude of nonlinear uncertain systems (robust performance in the “L1” setting) can be improved by using the known absolute stability (“L2”) techniques