Global stability and finite L2m-gain of saturated uncertain systems via piecewise polynomial Lyapunov functions

In this technical note, we provide sufficient conditions for global asymptotic stability and global L2m gain estimation of linear systems subject to saturations and/or deadzones with structured parametric uncertainties, based on piecewise polynomial Lyapunov functions. By using sum-of-squares relaxations, these conditions are formulated in terms of linear matrix inequalities. Example studies are used to comparatively illustrate the proposed techniques