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Robust reliable $$H_\infty$$ control for uncertain nonlinear systems via LMI approach. (English) Zbl 1141.93322
Summary: This paper investigates the robust reliable $$H_{\infty }$$ control for a class of uncertain nonlinear system. At first, a criterion for nonlinear system without uncertainties is proposed to guarantee global exponential stabilization and disturbance attenuation. Next, the criterion for uncertain nonlinear systems with parameter uncertainties is obtained by simple derivation. Linear Matrix Inequality (LMI) optimization approach is used to design the robust reliable $$H_{\infty }$$ state feedback control. Two numerical examples are given to illustrate the effectiveness of the main results.

##### MSC:
 93B35 Sensitivity (robustness) 93B36 $$H^\infty$$-control 93C10 Nonlinear systems in control theory 93C41 Control/observation systems with incomplete information 93D20 Asymptotic stability in control theory
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