Global stabilisation of linear systems with bounded controls by nonlinear feedback

A general nonlinear feedback law for global stabilisation of asymptotically null controllable linear systems with bounded controls is established. It is shown that such a nonlinear feedback law can be constructed in two recursive ways. The results effectively allow for the construction of a hybrid control law which is partly of a nested saturation form and partly of a sum of saturations form, giving more flexibility to the designer. Using the recursive formulation, one can obtain a series of control laws containing the well-known nested type and parallel connections type laws as two special cases. Moreover, the eigenvalues corresponding to the linearised closed-loop system can be arbitrarily assigned within a certain region, which can be further used to improve the system performances. The possible ranges for the controller's parameters are extended with respect to existing results.