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**A note on observer design for one-sided Lipschitz nonlinear systems.**
*(English)*
Zbl 1186.93017

Summary: Observer design of a class of nonlinear systems is considered. Based on the one-sided Lipschitz condition, sufficient conditions for the existence of observers of the class of nonlinear systems are presented. A design method of the observer that is dependent on the solution of the linear matrix inequality is then presented. Furthermore, a gain matrix of the observer is given. The method given in this note makes the applicable class larger than that given in the literature. It should be noticed that the proposed method is applicable not only to the monotone nonlinearities and Lipschitz nonlinearities but also to the one-sided Lipschitz nonlinearities which are neither monotone nonlinearities nor usual Lipschitz nonlinearities. Finally, we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory.

### MSC:

93B07 | Observability |

93C15 | Control/observation systems governed by ordinary differential equations |

93C10 | Nonlinear systems in control theory |

### Keywords:

nonlinear system; one-sided Lipschitz condition; positive definite matrix; asymptotically stable estimates
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\textit{Y. Zhao} et al., Syst. Control Lett. 59, No. 1, 66--71 (2010; Zbl 1186.93017)

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### References:

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