Control for a class of non-linear singularly perturbed systems subject to actuator saturation

This study considers the control problem for a class of non-linear singularly perturbed systems (SPSs) subject to actuator saturation. A sufficient condition for the existence of state-feedback controllers to achieve a prescribed stability bound is proposed and the corresponding basin of attraction is estimated. Then a convex optimisation problem is formulated, by which an optimal controller can be obtained to achieve a prescribed stability bound and simultaneously maximise the estimate of the basin of attraction of the SPSs for any allowable singular perturbation parameter. Furthermore, a stability condition is established, which improves the existing stability bound analysis methods for a class of non-linear SPSs. Finally, examples are given to show the advantages and effectiveness of the obtained results.