In the first section the authors consider a system
where the matrix is Hurwitz and is a possibly discontinuous function which represents nonlinear uncertainties. The admissible functions belong to a set defined by the inequality
where is a given matrix. The parameter is thought of as a measure of the size of .
The maximal value of is identified by solving an optimization problem, with constraints expressed in the form of a linear matrix inequality.
In the second section the author considers the case where is not Hurwitz. Here, (1) is replaced by
and a solution is sought in feedback form. In the following sections the author considers systems which satisfy the matching condition. Finally, the results are applied to decentralized control and interconnected systems.