State feedback control of continuous systems with state saturation

This paper concerns the design of state feedback controller for continuous systems with state saturation to make sure that the closed loop systems are globally asymptotically stable. Both full state saturation and partial state saturation are considered. By means of row diagonally dominant matrix with negative diagonal elements, nonlinear state saturation function can be represented as a convex combination of some linear functions. Based on Lyapunov stability theorem, the design methods of state feedback law for systems are given. Two algorithms for controllers are developed to achieve the design methods above, and can be implemented by solving linear matrix inequalities (LMIs). In the end, the corresponding numerical examples are given to show the effectiveness of the proposed algorithms.