时滞不确定离散系统的鲁棒l2-l∞滤波

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.

Robust l2-l∞ Filter Design for Uncertain Discrete-Time State-Delayed Systems

This paper is concerned with the problem of full-order robust l2 -l∞ filtering for uncertain discrete-time systems with a single delay in the state. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain, entering into all the matrices of the system state-space model. Sufficient conditions are established in terms of linear matrix inequalities for the existence of filters guaranteeing a prescribed energy-to-peak disturbance attenuation level for all possible uncertainties and time delays. And the admissible filter can be found by solving a convex optimization problem with global convergence assured. A numerical example demonstrates the validity of the proposed filter design procedure.