Stability analysis of linear systems with saturating actuators

A class of linear systems with saturating actuators is investigated in this paper. Auxiliary functions W₂(ρ), W₃(ρ), W₄(ρ), ... W_n(ρ) are presented based on additive decomposition approach and the relationship among them is discussed. Consequently, the sufficient conditions are obtained for asymptotical stability of linear systems with saturating actuators. Furthermore, the paper gives optimal W_i(ρ) to make the domain of attraction larger and puts forward the algorithm to solve the largest domain. Finally, two numerical examples are implemented to show the effectiveness of the results.