This paper addresses the nonfragile sensor fault estimation problem for a class of two-dimensional (2-D) nonlinear systems. The underlying system is described by the well-known Fornasini–Marchesini model. The system parameters are subject to abrupt changes regulated by the Markovian process for which the entries of the mode transition probability matrix are partially accessible. A novel 2-D nonfragile state estimator is constructed to achieve the sensor fault estimation where the estimator gains are allowed to be randomly perturbed. Then, together with the Lyapunov stability theory, the stochastic analysis techniques are employed to derive the sufficient conditions that guarantee the following three performance requirements: 1) the exponential stability of the estimation error dynamics; 2) the prespecified constraint on the energy-to-peak gain; and 3) the prespecified restriction on the prescribed power bound. Moreover, the estimator gains are parameterized by using the convex optimization method. Finally, a numerical example is provided to illustrate the effectiveness of the addressed estimation algorithm.

中文翻译：

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具有指定功率界限的马尔可夫跳跃二维系统的非脆弱 l2-l∞ 故障估计

本文解决了一类二维 (2-D) 非线性系统的非脆弱传感器故障估计问题。底层系统由著名的 Fornasini-Marchesini 模型描述。系统参数会受到由马尔可夫过程调节的突然变化的影响，其中模式转换概率矩阵的条目是部分可访问的。构建了一种新颖的二维非脆弱状态估计器来实现传感器故障估计，其中允许随机扰动估计器增益。然后，结合李雅普诺夫稳定性理论，采用随机分析技术推导出保证以下三个性能要求的充分条件：1）估计误差动力学的指数稳定性；2) 能量峰值增益的预设约束；3) 对规定权力界限的预先规定限制。此外，估计器增益通过使用凸优化方法进行参数化。最后，提供了一个数值例子来说明所寻址的估计算法的有效性。