Abstract
The analysis of the local stability in polyhedral sets of linear continuous-time systems with saturating controls is addressed. Two approaches are presented. The first one is based on a representation of the saturated system by a polytopic system. The second one consists in dividing the state space in regions of saturation. In each region of saturation the system evolution can be represented by a specific linear system with an additive disturbance. From these two representations conditions to the polyhedral contractivity with respect to the saturated closed-loop system are stated. These conditions guarantee the local stability of the closed-loop system when the polyhedral set is compact. The analysis of the stability when the polyhedron is not compact is also discussed.
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