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Robust finite-time $$H_\infty$$ control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. (English) Zbl 1395.93128
Summary: Robust finite-time $$H_\infty$$ control of a class of continuous-time nonlinear system with parameter uncertainties and disturbance input is discussed in this note. The nonlinear function is considered to satisfy the one-sided Lipschitz condition, which has less conservative than the well-known global Lipschitz nonlinear condition. By means of linear matrix inequality (LMI) techniques, both design algorithms of state-feedback controller and static output-feedback controller are developed. The designed controllers are proved to guarantee the corresponding closed-loop systems that are finite-time boundedness (FTB) with a desired $$H_\infty$$ performance index. And the best scalars selection criterion is used to determine the finite-time scalars such that the LMI-based conditions with the best feasibility in the global field. Finally, a numerical example is included to verify the efficiency of the proposed methods.

##### MSC:
 93B07 Observability 93C10 Nonlinear systems in control theory 93B52 Feedback control 93C15 Control/observation systems governed by ordinary differential equations 93C55 Discrete-time control/observation systems 93B36 $$H^\infty$$-control 93C41 Control/observation systems with incomplete information 93C73 Perturbations in control/observation systems
RODAS
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