New approach to robust observer-based control of one-sided Lipschitz non-linear systems

This study investigates the problem of robust observer design for a class of one-sided non-linear continuous-time systems with parameter uncertainties and $L_{2}$L2 bounded admissible external disturbance. The one-sided Lipschitz and quadratically inner-bounded conditions have been utilised to derive less conservative synthesis condition for the observer design. The corresponding design methodology is established, with the help some special derivations, bilinear matrix inequalities are successfully transformed into a set of linear matrix inequalities. Then, the robust controller and observer gains can be simultaneously found at one step. Finally, two numerical examples are given to illustrate the validity and the effectiveness of the proposed method.