Nonlinear observer design for one-sided Lipschitz systems
Nonlinear observer design for one-sided Lipschitz systems
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DOI：
10.1109/acc.2010.5530715
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发表时间：
2010-07
期刊：
影响因子：
--
通讯作者：
M. Abbaszadeh;H. Marquez
中科院分区：
文献类型：
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作者：
M. Abbaszadeh;H. Marquez
三十年来，满足Lipschitz连续性条件的非线性系统的控制和状态估计一直是非线性系统理论中的一个重要课题，产生了大量的文献。然而，这种方法背后的主要批评是Lipschitz连续性条件的限制性和相关结果的保守性。本文通过引入一类更一般的非线性函数，即单侧Lipschitz函数，对这一问题进行了扩展。所对应的一类系统是其著名的Lipschitz对应物的超集，在保守性方面具有固有的优势。本文首先建立了这类系统的状态观测器设计问题，讨论了存在的问题，并给出了一些面向分析的工具。然后，提出了用非线性矩阵不等式求解观测器设计问题的方法，将非线性矩阵不等式转化为数值上有效可解的线性矩阵不等式。
Control and state estimation of nonlinear systems satisfying a Lipschitz continuity condition have been important topics in nonlinear system theory for over three decades, resulting in a substantial amount of literature. The main criticism behind this approach, however, has been the restrictive nature of the Lipschitz continuity condition and the conservativeness of the related results. This work deals with an extension to this problem by introducing a more general family of nonlinear functions, namely one-sided Lipschitz functions. The corresponding class of systems is a superset of its well-known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. In this paper, first the problem of state observer design for this class of systems is established, the challenges are discussed and some analysis-oriented tools are provided. Then, a solution to the observer design problem is proposed in terms of nonlinear matrix inequalities which in turn are converted into numerically efficiently solvable linear matrix inequalities.