Further Result on the Observer Design for One-Sided Lipschitz Systems
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Further Result on the Observer Design for One-Sided Lipschitz Systems YANG Ming 1 ( ),
HUANG Jun 1∗ ( ),
ZHANG Wei 2 (
)
(1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou 215131, China; 2. Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai 201620, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: This paper investigates the problem of observer design for a class of control systems. Different from current works, the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz (OSL) condition but not quadratic inner-boundedness (QIB). Moreover, the case where the OSL constant is negative is specially investigated. Firstly, a full-order observer is constructed for the original system. Then, a reduced-order observer is also designed by using the decomposition method. The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation. Key words: control systems, one-sided Lipschitz (OSL) systems, full-order observers, reduced-order observers CLC number: O 231 Document code: A
0 Introduction In the past decades, the state estimation for nonlinear systems is a hot topic in the control community. The nonlinear dynamics are typically required to possess Lipschitz continuity. Thau[1] first considered the observer design problem for Lipschitz systems. After that, many works have been devoted to the so-called Lipschitz nonlinear observers[2-4] . The established methods in these works can only be applied to a class of systems with sufficiently small Lipschitz constants. In order to overcome the drawback, Hu[5] proposed the definition of one-sided Lipschitz (OSL) for the nonlinear observer design problem. Abbaszadeh and Marquez[6] proposed the definition of quadratic inner-boundedness (QIB), and sufficient conditions were presented by linear matrix inequalities (LMIs). By using S-procedure, Zhang et al.[7-8] improved the results of the previous work, and derived LMI conditions which were less conservative than those in Ref. [6]. Besides, there were many important works on observer design for positive systems, such as positive observer for linear positive systems[9] , and positive multi-mode observers for positive switched systems[10-11] . Following the line of Refs. [7] and [8], the synthesis problems of OSL systems were further investiReceived: 2019-10-30 Accepted: 2020-04-02 Foundation item: the National Natural Science Foundation of China (No. 61403267), and the China Postdoctoral Science Foundation (No. 2017M611903) ∗E-mail: [email protected]
gated[12-18] . By using stochastic theory, Barbata et al.[12] designed an exponentially stable observer for a class of stochastic OSL systems. Zhang et al.[13-14] focused on the observer framework of the systems with unknown input. Dong et al.[15] extended OSL condition to the nonlinear function with time delay. Based on the observer, Beikzadeh and Marguez[16] considered H∞ control probl
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