Maximal output admissible sets for discrete-time systems with disturbance inputs

The paper considers discrete-time linear systems with constrained disturbance inputs, w(t)∈Y⊂R^m, t∈Z⁺, and constrained outputs, y(t)∈Y⊂R^p, t∈Z⁺. An initial state of the system, x(0)∈Rⁿ, is output admissible if the output constraint is satisfied for all inputs meeting the input constraint; the set of all such states is the maximal output admissible set, O_∞. It is shown that O_∞ has basic properties that are similar to those which apply in the disturbance-free case. Procedures for computing O_∞ when Y is a polyhedron are available. The set O_∞ has important applications, including the determination of regions of attraction for linear closed-loop systems with actuator saturation