Robust stability for a class of nonlinear Lurie systems with unmatched uncertainties

In this paper, a strategy is established to design the robust controller for a class of continuous-time nonlinear systems with Lurie uncertainties.The uncertainty is decomposed into matched and unmatched components, and an augmented control is introduced for the unmatched uncertainty. An optimal control algorithm based on Hamilton-Jacobi-Bellman(HJB) equation is proposed for the design of a bounded robust controller and finite-time-horizon nonlinear systems. In this case, the robust control problem is transformed into the optimal control problem by properly choosing a cost function that reflects the uncertainties, regulation, and control. The bounded controller no longer requires the knowledge of the upper bound of systems uncertainty. A computable sufficient condition is also derived to ensure that the solution to the corresponding optimal control problem is a solution to the robust control problem. A simulation example is provided to verify the effectiveness under the present robust control scheme.