Estimation of basins of attraction for controlled systems with input saturation and time-delays

Basins of attraction are instrumental to study the effect of input saturation in control systems, as these sets characterise the initial conditions for which the control strategy induces attraction to the desired state. In this paper, we describe these sets when the open-loop system is exponentially unstable and the system is controlled by actuators with both constant time-delays and saturation. Estimates of the basin of attraction are provided and the allowable time-delay in the control loop is determined with a novel piecewise quadratic Lyapunov-Krasovskii functional that exploits the piecewise affine nature of the system. As this approach leads to sufficient, but not to necessary conditions for attractivity, we present simulations for two examples to show the applicability of the results.