Robust positive invariance and ultimate boundedness of nonlinear systems

In this article the problem of characterizing sets, described by vector nonlinear inequalities of the form v(x) ≤ w, as robustly positively invariant and targets of uniformly ultimate bounded nonlinear systems is investigated. The class of general parameter uncertain continuous-time dynamical systems affected by exogenous disturbances is considered. The approach is based on establishing an associated monotone nonlinear comparison system. A numerical example is presented to illustrate the approach.