Fuzzy H_∞ Filter Design for a Class of Nonlinear Systems with Time Delays via LMI

This paper develops fuzzy H_∞filter for state estimation approach for nonlinear discrete- time systems with multiple time delays and unknown bounded disturbances.We design a stable fuzzy H_∞filter based on the Takagi-Sugeno (T-S) fuzzy model,which assures asymptotic stability and a prescribed H_∞index for the filtering error system.Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem.The LMI problem can be efficiently solved with global convergence using the interior point algorithm.Simulation examples are provided to illustrate the design procedure of the proposed method.     

基于LMI的一类非线性多时滞系统的模糊H∞滤波器设计

This paper develops fuzzy H1 filter for state estimation approach for nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. We design a stable fuzzy H1 filter based on the Takagi-Sugeno (T-S) fuzzy model, which assures asymptotic stability and a prescribed H1 index for the filtering error system. Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem. The LMI problem can be efficiently solved with global convergence using the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the proposed method.     

模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

New approaches to robust Woo and H_∞ filtering for uncertain discrete-time systems

The problems of robust I2-I∞ and H∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed I2-I∞ or H∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.     

参数摄动系统的鲁棒H ∞状态估计

基于Shaked提出的参数依赖型有界实引理,研究具有凸多面体参数摄动系统的鲁棒H∞状态估计问题．采用线性矩阵不等式技术,推导出此类不确定系统的全阶鲁棒H∞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．与传统的基于二次稳定的滤波方案相比,该滤波器设计方法具有较小的保守性．     

第二FM模型的两维离散状态时滞系统H∞控制

This paper is concerned with the problem of H∞ control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state-space model. A sufficient condition to have an H∞ noise attenuation for this 2-D system is given in terms of a certain linear matrix inequality (LMI). The optimal H∞ controller is obtained by solving a convex optimization problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed result.     

一类非线性时滞系统的状态反馈镇定

The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.     

具有传输时延的网络控制系统故障估计与调节

In this paper, a method of fault estimation and fault tolerant control for networked control system (NCS) with transfer delay and process noise is presented. First, the networked control system is modeled as a multiple-input-multiple-output (MIMO) discrete-time system with transfer delays, process noise, and model uncertainties. Under this model and under some conditions, a fault estimation method is proposed to estimate the system faults. On the basis of the information on fault estimation and the sliding mode control theory, a fault tolerant controller is designed to recover the system performance. Finally, simulation results are used to verify the efficiency of the method.     

具有状态和测量时滞不确定系统的鲁棒H∞状态估计

考虑一类已知状态和测量时滞且范数有界参数不确定连续时间系统的鲁棒H∞状态估计问题.这个问题解的充分条件由二个代数Riccati不等式给出,它可以保证存在一个渐近稳定状态估计器使得对于所有不确定性从外界干扰到输出估计误差的传递函数满足指定的H∞指标.以上这些结果可以推广到一类未知状态和测量时滞且范数有界参数不确定连续系统的鲁棒H∞状态估计问题,对于已知状态和测量时滞系统,所得状态估计器与参数不确定性无关,而与时滞有关.对于未知状态和测量时滞系统,其状态估计器不仅与参数不确定性无关,而且与时滞也无关.     

第二FM模型的两维离散状态时滞系统H∞控制

本文研究了基于第二 FM 模型的两维离散状态滞后系统 H∞ 控制问题. 给出了这类两维系统具有一定 H∞ 扰动抑制度的一个线性矩阵不等式条件, 并通过求解一个凸优化问题得到一个最优 H∞ 控制器. 最后通过一个仿真例子验证所提结果的有效性.     

广义时滞系统时滞依赖H∞控制的改进结果

讨论广义时滞系统的时滞依赖控制问题. 基于线性矩阵不等式(LMI)方法和增广Lyapunov泛函, 给出保证系统正则、无脉冲、稳定且满足性能指标的时滞依赖有界实引理. 在此引理的基础上, 给出基于严格LMI的状态反馈控制器存在的时滞依赖条件. 同时给出所需状态反馈控制器的明确表示. 数值例子表明本文的结果改进了已有结论的保守性.     

不确定广义时滞系统的时滞依赖鲁棒H∞控制

讨论不确定广义时滞系统的时滞依赖鲁棒H∞控制问题. 基于线性矩阵不等式(LMI)方法, 设计状态反馈控制器使得对所有允许的不确定性, 所得的闭环系统均是正则、无脉冲、稳定且满足H∞范数有界约束. 所有的结论都是时滞依赖的且由不涉及系统矩阵分解的严格LMI表示. 数值例子表明所给的方法与已有的结论相比具有较小的保守性.     

区间变时滞不确定线性系统带记忆H∞状态反馈控制

一类存在范数有界不确定性的线性时变时滞系统, 其时变时滞仅给出时滞变化的上下界, 而对时滞变化率未作任何约束. 对于这类区间时变时滞系统, 给出了一种新型的 Lyapunov-Krasovskii 泛函讨论其稳定性, 通过分割平均时滞的方法减小保守性, 得到以线性矩阵不等式(LMI)形式给出的稳定性判据. 最后分析并给出了一种带记忆的 H∞ 状态反馈控制器. 数值实例表明了本文方法的有效性.     

量测缺失下多速率传感器系统的H∞滤波器设计

提出了一类具有量测缺失和堆栈存贮特性的网络化多速率系统的H∞滤波问题. 采用提升技术将多速率系统转化为单速率系统, 并提出了一种解决由提升所带来的因果约束的方法, 然后通过构造李亚普诺夫稳定函数设计H∞滤波器. 在构造滤波器过程中, 发现采样速率越慢, 滤波设计的保守性越强. 算例表明了方法的有效性, 并且分析了不同采样周期以及不同的量测到达率对滤波器性能的影响.     

基于Krein空间的线性离散时变系统H∞故障估计

研究一类受L2范数有界未知输入影响的线性离散时变系统H∞故障估计问题. 首先将系统H∞故障估计归结为二次型最小化问题, 然后引入相应的Krein空间系统, 应用Krein空间Kalman滤波理论, 推导并证明H∞故障估计问题可解的充要条件, 给出基于矩阵Riccati方程的H∞故障估计器设计, 为故障估计问题提供新的理论方法, 并通过算例验证本文提出方法的有效性.     

一类不确定切换奇异系统的动态输出反馈鲁棒H∞控制

研究一类由任意有限多个不确定子系统组成的切换奇异系统的动态输出反馈鲁棒H∞控制问题. 利用共同 Lyapunov 函数方法和凸组合技术, 给出由矩阵不等式表示的控制器存在的充分条件, 并设计了相应的子控制器和切换策略. 采用消元法, 将该矩阵不等式转化为一组线性矩阵不等式 (LMIs). 最后, 数值实例验证了所提方法的有效性.     

一类随机混杂系统的鲁棒方差控制

对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性.     

Delta算子系统具有圆形区域极点约束的非脆弱H∞滤波器设计: 一种LMI优化方法

研究了一类Delta算子线性系统具有圆形区域极点配置的非脆弱 H∞滤波器设计问题. 本文的目的是设计滤波器使得滤波误差系统不仅满足给定的圆点极点约束或D稳定约束, 而且从扰动输入到滤波误差的传递函数满足给定的 H∞范数约束. 所设计的滤波器具有乘性的滤波器增益变化, 基于Lyapunov稳定性理论和线性矩阵不等式方法, 给出具有区域极点配置的Delta算子离散系统非脆弱 H∞滤波器存在的充分条件. 数值仿真例子说明设计方法的有效性以及所提设计方法具有更小的保守性.     

参数不确定离散奇异系统的鲁棒H∞控制

研究了不确定离散奇异系统的鲁棒H∞控制问题, 控制目标是设计一个状态反馈控制器, 对所有允许的不确定性, 闭环系统正则、因果、稳定且具干扰衰减度γ. 首次提出了该问题的充分必要条件, 并且设计方法归结为求一个严格线性矩阵不等式(LMI)的可行性问题. 最后, 通过一个数值实例证实了该方法的有效性.