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

The paper considers discrete-time linear systems with constrained disturbance inputs, w(t)/spl isin/Y/spl sub/R/sup m/, t/spl isin/Z/sup +/, and constrained outputs, y(t)/spl isin/Y/spl sub/R/sup p/, t/spl isin/Z/sup +/. An initial state of the system, x(0)/spl isin/R/sup n/, 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/sub /spl infin//. It is shown that O/sub /spl infin// has basic properties that are similar to those which apply in the disturbance-free case. Procedures for computing O/sub /spl infin// when Y is a polyhedron are available. The set O/sub /spl infin// has important applications, including the determination of regions of attraction for linear closed-loop systems with actuator saturation.