Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model

Two integrator backstepping designs are presented for digitally controlled continuous-time plants in special form. The controller designs are based on the Euler approximate discrete-time model of the plant and the obtained control algorithms are novel. The two control laws yield, respectively, semiglobal-practical stabilization and global asymptotic stabilization of the Euler model. Both designs achieve semiglobal-practical stabilization (in the sampling period that is regarded as a design parameter) of the closed-loop sampled-data system. A simulation example illustrates that the obtained controllers may sometimes be superior to backstepping controllers based on the continuous-time plant model that are implemented digitally.