Asymptotic stability of a class of inherently nonlinear systems under linear feedback control

The asymptotic stability of a class of inherently nonlinear systems under linear feedback control is investigated. It is proved that, as long as all the linear feedback gains are positive, the considered nonlinear system under linear feedback control is asymptotically stable. Since only the positivity instead of the exact values of the feedback gains is required, the linear feedback controller is non-fragile. Moreover, it is shown that the linear feedback controller is also robust to some kind of uncertainties of the controlled system.

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