On the computation of an upper bound on the gap metric for a class of nonlinear systems

This work deals with the computation of upper bounds on the gap metric and the corresponding stability margin. The suggested bounds can be computed for a class of a nonlinear systems which satisfy an inequality. Comparing to previous works, where results are highly dependent on the studied cases, our methods are applicable to a wider range of nonlinear systems. The results are based on two inequalities derived for the gap metric and the stability margin with respect to the gain of the relevant systems. An example is provided to illustrate the derived bounds for both our method and a previous method that is based on the direct computation.