Convex Optimization Approaches to Robust ℒ1 Fixed-Order Filtering for Polytopic Systems with Multiple Delays

This paper investigates the robust ℒ₁ fixed-order filtering problem for continuous polytopic systems with multiple state delays. Attention is focused on the design of robust full-order and reduced-order filters that guarantee the filtering error system to be asymptotically stable and satisfy the worst case peak-to-peak gain of the filtering error system for all admissible uncertainties and time delays. In particular, we concentrate on the delay-dependent case, and the peak-to-peak performance criterion is first established for polytopic systems with multiple state delays. Two different convex optimization approaches are proposed to solve this problem. One is the parameter-dependent Lyapunov approach in which the filter is not only dependent on the parameters (residing in a polytope), but also the Lyapunov matrices are different over the entire polytope domain. The other is the quadratic stability approach which obtains an admissible filter in the quadratic framework. Computational algorithms in terms of linear matrix inequalities (LMIs) are provided. It is shown that the parameter-dependent Lyapunov approach turns out to be less conservative than the quadratic stability approach, but the quadratic stability approach is computationally less demanding. Two numerical examples are presented to illustrate the proposed theory. This work was partially supported by RGC HKU 7028/04P, the Natural Science Foundation of Heilongjiang Province under Grant F200504, and the Scientific and Technical Research Project of the Education Department of Heilongjiang Province under Grant 10551013.     

It?型Markov切换系统时滞相关指数稳定性

研究了时变时滞满足h1≤d(t)≤h2的It型随机Markov切换系统的区间时滞相关指数稳定性.通过构造不同的Lyapunov-Krasovskii函数,并通过引入一些改进的积分等式方法,以线性矩阵不等式的形式提出了具有较小保守性的区间时滞依赖指数稳定性条件.最后通过数值算例说明本文结论的有效性及具有较低的保守性.     

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

l2-l∞ filter design for discrete-time singular Markovian jump systems with time-varying delays

The problem of l₂-l_∞ filter design for discrete-time singular systems with Markovian jump and time-varying delays is investigated in this paper. By using the delay partitioning technique, a delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l₂-l_∞ performance index. Based on the derived condition, the full-order and reduced-order filters with mode-independent characterization are designed in a unified framework. The corresponding filter parameters can be obtained by solving a set of linear matrix inequalities. The reported results not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

基于T-S的时滞模糊系统的鲁棒稳定与镇定问题

讨论同时具有输入及状态时滞且多个范数有界不确定的非线性时滞模糊系统的时滞相关鲁棒稳定及镇定问题。利用通用的Lyapunov—Krasovskii泛函方法,结合自由权矩阵思想和对不确定项的更精确描述,获得基于线性矩阵不等式的时滞相关稳定的充分条件并给出状态反馈控制器的设计。该条件较已有结论不仅形式简单,而且具有更小的保守性。利用Matlab软件中的LMI工具箱求解,得到保证系统鲁棒渐近稳定的最大可允许时滞上界。数值算例表明该方法是有效性的。     

基于切换模糊模型和分段Lyapunov函数的T-S模糊系统时滞依赖H∞控制

研究了离散时滞T-S模糊系统的H无穷控制问题. 首先, T-S模糊系统被转换成等价的切换模糊系统, 基于分段Lyapunov函数, 给出了该系统带有H无穷性能的时滞依赖稳定化控制方法. 所得结论可以用一组线性矩阵不等式表示. 由于考虑了子系统间的相互关系, 因此所得结论较以往结果具有更小的保守性. 最后, 仿真例子说明了所提方法的有效性.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

具有时变时滞的Lurie系统绝对稳定性的时滞相关条件

Some delay-dependent absolute stability criteria for Lurie control systems with time-varying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples are provided to demonstrate the effectiveness of the proposed methods.     

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.     

Lurie型时滞系统的稳定性与镇定

研究了Lurie时滞系统的绝对稳定性问题，导出了用一个线形矩阵不等式系统的可行性表示的时滞依赖绝对稳定性判据，进而通过求解线性矩阵不等式，给出使得闭环系统绝对稳定的无记忆状态反馈控制器设计方法，最后用仿真例子验证了文中所提出的结果。