Nonlinear H∞ observer design for one-sided Lipschitz systems

Abstract This paper is considered with the H ∞ observer design problem for a class of nonlinear systems with the one-sided Lipschitz condition. The systems under consideration include the well-studied Lipschitz system as a special case and possess inherent advantages with respect to conservativeness. For such systems in the presence of noises, we develop a Linear Matrix Inequality (LMI) based approach to design a nonlinear H ∞ observer by carefully dealing with the one-sided Lipschitz condition together with the quadratic inner-bounded condition. The resulting nonlinear H ∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed H ∞ performance. Moreover, for the design purpose, the existence condition of the proposed nonlinear H ∞ observer is formulated in terms of LMIs by using a matrix generalized inverse technique. Finally, a simulation example is given to illustrate the effectiveness of the proposed design.

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