Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input-additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing H₂-type gain scheduling controller, which requires the online solution of a state-dependent nonlinear optimization problem and a state-dependent H₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input-additive uncertainties, the proposed controller also partially recovers Teel's H_∞-type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The H_∞-type scheduling approach achieves robustness not only with non-inputadditive uncertainties but also requires the closed-form solution to an H_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the H_∞-type scheduling approach in the absence of non-input-additive uncertainties.