Local lp-stability and local small gain theorem for discrete-time systems (vol 41, pg 903, 1995)

Section VI of the local lp-stability and local small gain theorem for discrete-time systems contains an error. The system Σd y(t+1) = f(y(t-h), ···, y(t-1),y(t))+u(t) is considered. The system is proved that: it can be improved, replacing lp-observability by a novel notion called lp-constructibility. In the linear case, this notion is equivalent to the usual constructibility. Σd is globally lp-observable must be replaced with Σd is globally lp-constructible. It is further proved that zero is a locally asymptotically stable equilibrium point for the unforced system associated with Σd.