Explicit Formulas for ISS Stabilization of Nonlinear Systems Subject to Bounded Inputs and Disturbances

Control Lyapunov functions (CLFs), CLF based controller designs and disturbance attenuation have attracted much attention in nonlinear control theory. However, little research exists that considers both the input constraint and the disturbance attenuation problems. For input constrained systems, we cannot stabilize under unbounded disturbances in general. Therefore, we propose an input-to-state stabilizable robust control Lyapunov function (ISS-RCLF) and an asymptotically stabilizable robust control Lyapunov function (AS-RCLF) for an input-restricted nonlinear system. In this paper, we propose a stabilizing controller for input and disturbance constrained nonlinear systems using ISS-RCLF, which becomes continuous if an ISS-RCLF has an ISS-CLF small control property. Moreover, we clarify the condition to be satisfied for an AS-RCLF and an ISS-RCLF, and when a proper function becomes an ISS-RCLF. Finally, we show the effectiveness of the proposed method by computer simulation.