An ARE approach to semi-global stabilization of discrete-time descriptor linear systems with input saturation

The semi-global stabilization problem of discrete-time descriptor linear systems with input saturation is considered. By exploring the properties of the solutions to a class of parametric discrete-time Riccati equations for discrete-time descriptor linear system and their associated feedback gains, both the state feedback and output feedback semi-global stabilization problem are solved by linear feedback without any system decomposition on the original descriptor linear system. A numerical example is used to show the effectiveness of the proposed approach.