Sampled-data control for nonlinear systems with mismatched disturbances via a non-recursive design framework

In this paper, a sampled-data state feedback controller based on a non-recursive design framework is proposed for a class of nonlinear lower triangular systems with mismatched disturbances. Firstly, the continuous-time observer is discretized by the Euler method, and the continuous-time controller is discretized by the zero-order holding method. Then, by constructing a reasonable Lyapunov function and applying Gronwall-Bellman inequality, it has been rigorously demonstrated that the global bounded stability of the closed-loop system can be guaranteed by a appropriate selection of sampling period and scaling gain. By employing the non-recursive method, the proposed scheme avoids the problem of " explosion of terms " caused by recursive design procedures. In the meantime, a new discrete-time observer is designed to observe the disturbance of the sampling points given the adverse effects of the mismatched disturbances. Since both the observer and the controller are discrete in form, they are easy to implement on a digital computer. The efficacy of the proposed control scheme is validated through numerical simulations.