Abstract
Grüne et al. (2008) proposed a digital control law approximating the response of a nonlinear continuous-time controlled system. In this research, we improve the Grüne's controller to allow one sampling delay for the calculation time digital computers. Moreover, we focus on only a control Lyapunov function of which accuracy should be maintained. We show that Sontag-type controller satisfies the necessary and sufficient condition of the applicability of the proposed controllers. In addition, we establish a monotonic decrease of a Lyapunov function on any compact set except a neighbourhood of the origin to show the semiglobal practical uniform asymptotical stability of the closed loop system for the proposed method.
