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将l2 -l∞ 性能指标引入时滞不确定离散时间系统 ,研究基于这一指标的滤波器设计问题 .所研究的对象是同时具有状态时滞和多面体不确定性的离散时间系统 .采用线性矩阵不等式技术推导了此类不确定系统鲁棒l2 -l∞ 滤波器存在的充分条件 ,并将滤波器的设计转化为一个凸优化的求解问题 ,可以采用较为有效的内点方法进行求解 .所设计的滤波器能够保证相对于所有能量有界的外界扰动信号 ,滤波误差系统具有一定的l2 -l∞ 扰动衰减水平 .数值仿真验证了所提出算法的可行性 .
The l2-l∞ performance index is introduced into the discrete-time uncertain system with time-delay, and the filter design problem based on this index is studied. The research object is a discrete-time system with both state delay and polytopic uncertainty. Inequality technique derives sufficient conditions for the existence of robust l2 -l∞ filters for such uncertain systems, and transforms the filter design into a convex optimization problem, which can be solved by the more effective interior point method. The filter can guarantee the perturbation signal with respect to all energy bounded outside and the filtering error system has a certain level of l2-l∞ disturbance attenuation.The numerical simulation shows the feasibility of the proposed algorithm.