Stability analysis of singularly perturbed control systems with actuator saturation

Stability of singularly perturbed systems (SPSs) with actuator saturation is investigated. A set invariance condition with guaranteed stability bound is proposed. Based on this condition, two optimization problems are formulated separately. One is used to get the best estimate of the stability bound with guaranteed basin of attraction, while the other is used to get the best estimate of the basin of attraction with guaranteed stability bound. The proposed algorithms to solve the optimization problems are independent of the singular perturbation parameter and thus well conditioned. Two examples are included to show the advantages and effectiveness of the proposed results.