In the first section the authors consider a system $$\dot x= Ax+ h(t,x),\tag 1$$ where the matrix $A$ is Hurwitz and $h(t,x)$ is a possibly discontinuous function which represents nonlinear uncertainties. The admissible functions $h(t,x)$ belong to a set $H_\alpha$ defined by the inequality $$h(t,x)^T h(t,x)\le \alpha^2 x^T H^T Hx,$$ where $H$ is a given matrix. The parameter $\alpha$ is thought of as a measure of the size of $H_\alpha$.
The maximal value of $\alpha$ 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 $A$ is not Hurwitz. Here, (1) is replaced by $$\dot x= Ax+ Bu+ h(t,x)\tag 2$$ 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.