Analysis and Stabilization of Linear Cone-Preserving Systems With Bounded Inputs

This paper focuses on estimating the domain of attraction for linear cone-preserving systems subject to saturated linear feedback. The considered system model belongs to a category of control systems whose state trajectories are constrained within proper cones. In terms of cone max norms induced by proper cones, an extended max-separable Lyapunov function is constructed. Furthermore, sufficient criteria are given to show that the level set of this Lyapunov function is contractively invariant for the closed loop through the reproducing property of proper cones, and the controller to enlarge this set is synthesized via iterative algorithms. For the single-input case, we show that once the direction of the upper bound vector of the contractive invariant set is determined, an exact characterization of the maximal contractively invariant set can be given. Finally, two numerical examples are provided to verify the validity of the results.