On semiglobal stabilization of linear systems with input saturation using a multiple parametric Lyapunov approach

There are currently three approaches to construct a parameterized family of stabilizing feedback gains: the eigenstructure assignment approach, the parametric algebra Riccati equation based approach and the parametric Lyapunov equation based approach. The third method possesses the advantages of the first two and results in both an explicitly parameterized feedback gain and a Lyapunov function. However, the number of parameters is limited. In this paper, we discuss another method based on solutions of multiple Lyapunov equations, which takes advantage of the parametric Lyapunov equation based approach, and has multiple adjustable parameters to achieve complex system performance requirements. The proposed method not only gives some corresponding results for the parametric Lyapunov equation, but also reveals some important intrinsic properties. Moreover, we develop the proposed method to feedback gains design for linear systems with input saturation. Finally, one illustrative example is provided to demonstrate the advantage as well as the effectiveness of the obtained results.