Additional material to the paper ’ Norm - controllability of nonlinear systems ’

This technical report contains some additional calculations supplementing Example 6 in the paper Normcontrollability of nonlinear systems by M. A. Müller, D. Liberzon, and F. Allgöwer, IEEE Transactions on Automatic Control, 2015. References and labels in this technical report (in particular Equation labels (1)–(59) and all theorem numbers etc.) refer to those in that paper. In the following, consider a fixed initial condition x0 = [x1(0) x2(0)] T ∈ R≥0 \ B, which means that x2(0) > (k/c)x1(0) 2. For a constant input u = b > 0, the (unique) equilibrium of system (34) is given by x1,s(b) := (c/2k) (