| annote | = | {The problem of Set-membership State Estimation (SSE) is addressed. The work focuses on the main advantages and drawbacks of this kind of methodology. The theoretical background needed for developing a strategy using SSE is given (principle of convex sets theory, operation between sets and properties). Parallelotopes, and polytopes are deeply studied in the context of SSE. The most important properties and operations of the previous sets, together with their demonstrations, and also examples are given. New approaches are proposed. This is the case, for the intersection of parallelotopes, Minkowski sum, intersection and linear transformation of polytopes. A generalization of SSE approach is given taking into consideration a linear system that is found by the decomposition of a nonlinear system and various outputs signals. Moreover, two algorithms have been established to perform an SSE approach using parallelotopes or polytopes. A robust MPC control strategy is used to show the results with parallelotopes. Finally, a set of conclusions and futures challenges is given.}, |