Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

This paper deals with control systems subject to backlash and saturation in the loop. One of the goals is to characterize, or at least to approximate, the attractor of such nonlinear dynamical systems. Then, the regional or global asymptotic stability of the closed loop with respect to this attractor is handled. An anti-windup inspired loops is added aiming at improving the quality of the attractor approximation in which converge the closed-loop trajectories and of the basin of attraction of such an attractor. Numerically tractable algorithms with feasibility guarantee are provided, as soon as the linear closed-loop system, obtained by neglecting the backlash and saturation effects, is asymptotically stable. The interest of the results is drawn through an illustrative example.