AI 中文总结
针对受扰非线性广义系统，传统 H_infinity 滤波方法有局限。本文提出在显式状态空间框架中构建泛函 H_infinity 滤波器，利用增量二次约束表征非线性，通过秩条件和线性矩阵不等式建立准则，降低计算复杂度，经模拟验证了方法有效性。
AI 中文摘要
本文为受外部干扰的非线性广义系统开发了一种泛函 H_infinity 滤波器。传统的广义系统 H_infinity 滤波方法有严格的正则性假设且采用隐式广义形式滤波器，存在实际实现困难，现有方法主要针对全阶或降阶状态估计，当只需特定状态泛函时计算效率低。本文滤波器直接在显式状态空间框架中构建，可任意初始化，阶数小于或等于待估计泛函向量维度以降低计算复杂度。用适当乘子矩阵参数化的增量二次约束表征非线性，通过对系统矩阵施加秩条件和一组线性矩阵不等式建立滤波器存在的充分准则。在此条件下保证估计误差动态的渐近稳定性，外部干扰对误差的影响在规定的 L2 性能框架内有界。最后通过数值模拟验证了理论结果的有效性。
英文摘要
This paper develops a functional H_infinity filter for nonlinear descriptor systems subject to external disturbances. Conventional H_infinity filtering approaches for descriptor systems impose restrictive regularity assumptions and employ implicit descriptor-form filters, leading to practical implementation difficulties. Moreover, existing approaches mainly target full-or reduced-order state estimation, which is computationally inefficient when only a specific functional of the state is required. To address these limitations, the filter is formulated directly in an explicit state-space framework and can be initialized with arbitrary initial values. The filter order is chosen to be less than or equal to the dimension of the functional vector to be estimated, thereby reducing computational complexity. The considered nonlinearities are characterized using incremental quadratic constraints parameterized by appropriate multiplier matrices, which encompass Lipschitz, one-sided Lipschitz, monotone, and many other nonlinearities. Sufficient criteria for the existence of the proposed filter are established through a rank condition imposed on the system matrices together with a set of linear matrix inequalities (LMIs). Under these conditions, asymptotic stability of the estimation error dynamics is guaranteed, while the influence of external disturbances on the error is bounded within a prescribed L2-performance framework. Finally, numerical simulations demonstrate and validate the effectiveness of our theoretical results.
CommentsExtended version of the paper accepted for publication in the IEEE Open Journal of Control Systems. Includes an additional appendix omitted from the published version due to space constraints
