Robust control of linear systems under input saturation using Barrier Lyapunov functions

This paper deals with the robust stabilization of input saturated uncertain linear systems with perturbed measurements. The controller designed as a linear output feedback allowed to characterize the region of attraction where the initial conditions must belong in order to guarantee the asymptotic convergence of the system trajectories into a ultimately bounded region around the origin. The stability analysis employed the concept of Barrier Lyapunov functions (BLF) and the attractive ellipsoid method (AEM) to find sufficient conditions in terms of linear matrix inequalities characterizing the ultimate bounded region of attraction. The methodology proposed is to use the BLF to estimate the region of attraction, while the AEM successfully characterized the ultimately bound. And optimization procedure maximized the set estimating (in some sense) the region of attraction and minimized the ultimate bounded set. Simulation results showed the accuracy in the estimation of the region of attraction and the minimal ellipsoid characterization.