Computation of polyhedral H-invariant sets for saturated systems

In this paper, a unified approach to the estimation of the domain of attraction of a saturated linear system is presented. We show how to choose a linear difference inclusion (LDI) in such a way that the conservativeness in the estimation is reduced. We provide an algorithm that estimates the domain of attraction of the nonlinear system. Under mild assumptions, the proposed algorithm obtains a polyhedral invariant set that equals the maximal domain of attraction for the linear difference inclusion. An alternative approach, that obtains a sequence of invariant sets with a reduced number of constraints, is also proposed.