Robust finite-time H∞ control for one-sided Lipschitz nonlinear systems via state feedback and output feedback

Robust finite-time H∞ control of a class of continuous-time nonlinear system with parameter uncertainties and disturbance input is discussed in this note. The nonlinear function is considered to satisfy the one-sided Lipschitz condition, which has less conservative than the well-known global Lipschitz nonlinear condition. By means of linear matrix inequality (LMI) techniques, both design algorithms of state-feedback controller and static output-feedback controller are developed. The designed controllers are proved to guarantee the corresponding closed-loop systems that are finite-time boundedness (FTB) with a desired H∞ performance index. And the best scalars selection criterion is used to determine the finite-time scalars such that the LMI-based conditions with the best feasibility in the global field. Finally, a numerical example is included to verify the efficiency of the proposed methods.