不确定连续系统的鲁棒L2-L∞滤波新方法

借助投影定理提出了一个新的连续系统L2-L∞性能准则.与已有的判据相比,该准则 呈现出Lyapunov矩阵与系统矩阵之间分离的特性,使得将其应用于不确定系统时能够得到参 数依赖型Lyapunov函数.利用该判据,采用线性矩阵不等式技术推导了多面体不确定系统的全 阶和降阶鲁棒L2-L∞状态估计新方法.所提出的方法可被进一步用于研究具有极点约束的L2-L∞ 滤波问题.与已有的基于二次稳定的滤波方案相比,本文提出的方法具有较低的保守性.

New Approach to Robust L2-L∞ Filter Design for Uncertain Continuous-Time Systems

With the help of Projection Lemma, a new L2- L∞ performance criterion is derived,which exhibits a kind of decoupling between Lyapunov matrix and system matrices. This kind of decoupling is enabled by introduction of an additional slack variable and enables us to obtain a parameter-dependent Lyapunov function for polytopic uncertain systems. Upon the proposed performance condition and by means of linear matrix inequality technique, both full-order and reduced-order robust L2-L∞ filtering problems are solved in a unified framework. The proposed approach can be further extended to deal with filtering problems with pole constraint. Compared with earlier result in the quadratic framework, our approach turns out to be less conservative.