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Robust stabilization of nonlinear systems: The LMI approach. (English) Zbl 0968.93075
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 $h(t,x)^T h(t,x)\leq \alpha^2 x^T H^T Hx,$ 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.

##### MSC:
 93D21 Adaptive or robust stabilization 93D09 Robust stability 93A14 Decentralized systems 93C73 Perturbations in control/observation systems
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