Robust Control for State Constrained Uncertain Systems: Attractive Ellipsoid Method Approach

A robust control feedback strategy is developed to solve the stabilization problem of constrained systems with uncertainties and output perturbations. The states are assumed to be constrained inside a given polytope and the perturbations bounded. The control law is developed using an extended version of the attractive ellipsoid method (AEM) approach, and a barrier Lyapunov function (BLF); this is a function whose value goes to infinity whenever its arguments approach to the boundary of a given set. The control parameters are obtained through the solution of some optimization problems related to the approximation of the constraints set and the characterization of a minimal ultimate bounded set for the system trajectories. The implementability of the resulting algorithm is supported by a numerical example and by the comparison with the regular AEM based on a quadratic Lyapunov function.