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An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

The problem of designing an observer for nonlinear Lipschitz systems affected by system and sensor noises is addressed. Related to the system nonlinearity, the stability of observer dynamic with static and dynamic gain is considered. The advantage of using dynamic gain to deal with large Lipschitz nonlinearity is discussed and it is proved that no dynamic gain can stabilise the observer for a larger Lipschitz constant as compared with the static gain. However, a nonlinear observer with dynamic gain has some additional degrees of freedom which can be utilised to attenuate noise effect on the observer behaviour. Using mixedandcriteria, this article introduces a method to obtain a dynamic gain which can deal with system nonlinearity and noise simultaneously. The effectiveness of the proposed method is finally demonstrated by some simulation results. [ABSTRACT FROM AUTHOR]

The problem of designing Luenberger-like observer for non-linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger-like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach. [ABSTRACT FROM AUTHOR]