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Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

机译：具有测量延迟的单侧Lipschitz非线性系统的观测器设计

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This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen's inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust against.. 2 norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality-(LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.
机译：本文针对存在输出延迟的单侧Lipschitz非线性系统提出了一种新颖的非线性观测器设计方法。该方法的关键是克服由于物理位置和工程非线性系统状态的估计而造成的时间延迟的实际后果，这些时间延迟是由于传感器位置遥远和测量中存在时间滞后而造成的。使用Lyapunov-Krasovskii泛函，其时间导数使用Jensen不等式，单侧Lipschitz条件和二次内界来求解，因此，设计了依赖于延迟范围的非线性时滞观测器的设计条件Lipschitz系统是派生的。此外，从目前的依赖于延迟范围的技术推导了针对单侧Lipschitz模型的延迟依赖的观察者综合问题以及线性和Lipschitz非线性系统的延迟范围依赖状态估计问题的新颖解决方案。设计了一种观察器公式化方法，用于检索单侧Lipschitz非线性系统状态，该方法对2个范数有界扰动具有鲁棒性。与传统方法相比，可以通过基于保守度较低的线性矩阵不等式（LMI-）的例程来解决所得的设计条件，该例程借助附加的LMI变量，有意义的变换和圆锥互补线性化算法而获得成功。数值算例说明了所提出的观测器综合方法对延迟单侧Lipschitz系统的有效性。

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