New results on stability margins of nonlinear discrete-time receding horizon h_∞ control

In this paper, we present some new results on stability margins of receding horizon H_∞ control for nonlinear discrete-time systems with disturbance. First, we propose a nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems with disturbance. Under this condition, noninceasing monotonicity of the saddle point value function of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures closed-loop internal stability. The proposed receding horizon H_∞ control guarantees the infinite horizon H_∞ norm bound of the closed-loop system. Under additional conditions, the global result and the input-to-state stable (ISS) property of the proposed receding horizon controller are also given. Finally, we derive new H_∞ stability and ISS margins for the proposed receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.