Piecewise polynomial Lyapunov functions for global asymptotic stability of saturated uncertain systems

In this paper we provide sufficient conditions for global asymptotic and global exponential stability of linear systems subject to saturations and/or deadzones. These conditions rely on piecewise polynomial Lyapunov functions and are formulated in terms of linear matrix inequalities, by using sum-of-squares relaxations. It is also shown that the proposed approach can be extended to deal with robust stability of saturated systems affected by structured parametric uncertainties. Example studies are presented to illustrate the reduced conservativeness of the proposed conditions as compared to existing results. © 2011 IFAC.