Networked H∞ filtering for linear discrete-time systems

This paper studies the problem of networked H_∞ filtering for linear discrete-time systems. A new model is proposed as the filtering error system to simultaneously capture the communication constraint, random packet dropout and quantization effects in the networked systems. A sufficient condition is presented for the filtering error system to be mean square exponentially stable with a prescribed H_∞ performance by employing the multiple Lyapunov function method. The obtained condition depends on some parameters of the networked systems, such as the access sequence of nodes, packet dropout rate and quantization density. With these parameters fixed, a design procedure for the desired H_∞ filter is also presented based on the derived condition. Finally, an illustrative example is utilized to show the effectiveness of the proposed method.     

Improved robust H2 and H∞ filtering for uncertain discrete-time systems

This paper is concerned with the robust H₂ and H_∞ filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H₂ or H_∞ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed H₂ or H_∞ performance and lead to a less-conservative design.     

具有随机采样特性的网络化系统H∞ 滤波

研究一类具有随机采样特性的网络化系统H∞滤波问题.通过将传感器的随机采样过程建模成马尔可夫链,将数据量化作用转化为模型的参数不确定性,并用二值随机变量描述丢包过程,从而用一个多随机变量的马尔可夫不确定性模型来描述滤波误差系统.应用Lyapunov稳定性理论和随机系统分析方法,导出了滤波误差系统随机稳定且具有给定H∞性能的充分条件,并给出了滤波器的设计方法.仿真结果验证了所提出方法的有效性.     

受复杂多通道通信约束的网络化系统H2/H∞滤波

多通道网络化系统中每个通道存在不尽相同的网络不确定性因素, 使得H₂/H_∞ 滤波更加困难. 对此, 提出一种受多通道通信约束的网络化系统滤波方法. 首先, 基于最大数据包错序思想解决了传感器到滤波器之间的复杂多通道通信约束的问题; 然后, 建立了更加普适的融合多通道通信约束的滤波误差动态系统模型, 证明了在已知最长网络延时和最大连续丢包数情况下, 所设计的滤波器可使系统随机稳定且满足??2/??∞ 性能指标. 仿真结果表明该方法可行且有效.

     

New results on H∞ filtering for fuzzy systems with interval time-varying delays

This paper investigates the problem of H_∞ filtering for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the delay partitioning idea, a new approach is proposed for solving this problem, which can achieve much less conservative feasibility conditions. The attention is focused on the design of an H_∞ filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the H_∞ attenuation level from disturbance to estimation error is below a prescribed scalar. The constructed Lyapunov-Krasovskii functional, by applying the delay partitioning method, can potentially guarantee the obtained delay-dependent conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. Finally, an example is illustrated to show the reduction in conservatism of the proposed filter design method.     

不确定线性时变时滞系统的鲁棒H∞ 滤波

研究一类不确定线性连续时滞系统的改进鲁棒H∞滤波问题.采用时滞分解方法,构造一种新的Lyapunov-Krasovskii泛函,并基于一种积分不等式讨论了确定性系统的H∞性能分析问题.然后,借助于线性化技术,以线性矩阵不等式(LMI)的形式给出了滤波器存在的充分条件,并将确定性系统滤波器设计方法扩展到凸多面体不确定性情形.最后通过仿真算例说明了该方法的有效性.     

Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty

The robust H_∞ filtering problem with error variance constraints is considered for discrete time-varying systems subject to norm-bounded parameter uncertainties in both the state and the output matrices of the state-space model. Sufficient conditions for a finite-horizon filter to satisfy state estimation error variance constraints as well as prescribed H_∞ performance for all admissible perturbations are given in terms of two discrete Riccati difference equations, which are of a form suitable for recursive computation. The results are extended to cover the case of stationary filtering over an infinite-horizon for uncertain time-invariant systems.     

Robust H∞ filtering for uncertain impulsive stochastic systems under sampled measurements

This paper is concerned with the problem of robust H_∞ filtering for uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is to design a stochastically stable filter, using the locally sampled measurements, which ensures both the robust stochastic stability and a prescribed level of H_∞ performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. An example is provided to demonstrate the effectiveness of the proposed approach.     

Networked H∞ control of linear systems with state quantization

This paper addresses the problem of H_∞ controller design for linear systems over digital communication networks. A new model is proposed to describe both the network conditions and the state quantization of the networked control systems in a unified framework. From this model, a quantized state feedback strategy is developed for global and asymptotical stabilization of the networked control systems. The same H_∞ disturbance attenuation level as that in the case without quantization is achieved. Numerical examples are given to demonstrate the effectiveness of the proposed method.     

Delay-dependent robust H∞ control for uncertain systems with a state-delay

A robust H_∞ control for uncertain linear systems with a state-delay is described. Systems with norm-bounded parameter uncertainties are considered and linear memoryless state feedback controllers are obtained. Firstly, a delay-dependent bounded real lemma for systems with a state-delay is presented in terms of linear matrix inequalities (LMIs). By taking a new Lyapunov-Krasovsii functional, neither model transformation nor bounding for cross terms is required to obtain delay-dependent results. Secondly, based on the bounded real lemma obtained, delay-dependent condition for the existence of robust H_∞ control is presented in terms of nonlinear matrix inequalities. In order to solve these nonlinear matrix inequalities, an iterative algorithm involving convex optimization is proposed. Numerical examples show that the proposed methods are much less conservative than existing results.     

网络化多胞型系统的变增益H∞ 控制

研究参数变化速率有界的网络化多胞型系统的变增益H_∞ 控制问题. 采用时滞状态增广方法处理状态传输时延, 得到切换多胞型系统模型; 考虑参数变化速率约束与参数传输时延影响, 给出对当前参数、次刻参数和时滞参数三元组的多胞描述方法; 进而基于参数依赖切换Lyapunov 函数方法给出变增益H_∞ 控制器的LMI 设计准则. 该方法将已有结果推广至包含网络传输时延的情形, 具有较低的保守性. 仿真实例表明了所提出方法的有效性.     

H2/H∞ Control of discrete singularly perturbed systems: the state feedback case

The design of a mixed H₂/H_∞ linear state variable feedback suboptimal controller for a discrete-time singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index both are O(ε) close to those synthesized using the full order system.     

Robust switching-type H∞ filter design for linear uncertain systems with time-varying delay

This paper is concerned with the problem of robust H_∞ filter design for a class of linear uncertain systems with time-varying delay. The uncertainty parameters are supposed to be time-varying, unknown, but bounded, which appear affinely in the matrices of the considered system model. Based on linear matrix inequality (LMI) method and switching laws, a new switching-type filter is designed to guarantee the asymptotic stability and H_∞ performance level of the filtering error systems. The key feature is that the new proposed filter parameters are switching between certain fixed gains automatically via the designed switching law. It is shown that the new filter design method is less conservative than the traditional fixed gain filter design method. An example is given to illustrate the validity of the proposed design.     

A mixed H2/H∞ adaptive tracking control for constrained non-holonomic systems

In this study, a PID type controller incorporating an adaptive control scheme for the mixed H₂/H_∞ tracking performance is developed for constrained non-holonomic mechanical systems under unknown or uncertain plant parameters and external disturbances. By virtue of the skew-symmetric property of the non-holonomic mechanical systems and an adequate choice of a state variable transformation, sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled non-linear differential equations. The coupled algebraic equations can be solved analytically.     

H∞ filtering for discrete-time systems with randomly varying sensor delays

This paper investigates an H_∞ filtering problem for discrete-time systems with randomly varying sensor delays. The stochastic variable involved is a Bernoulli distributed white sequence appearing in measured outputs. This measurement mode can be used to characterize the effect of communication delays and/or data-loss in information transmissions across limited bandwidth communication channels over a wide area. H_∞ filtering of this class of systems is used to design a filter using the measurements with random delays to ensure the mean-square stochastic stability of the filtering error system and to guarantee a prescribed H_∞ filtering performance. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a linear matrix inequality (LMI). Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

H∞ control of dead-time systems based on a transformation

This paper presents a transformation that makes all the robust control problems of dead-time systems able to be solved similarly as in the finite-dimensional situations. With trade-off of the performance, some advantages obtained are: (i) the controller has a quite simple and transparent structure; (ii) there are no any additional hidden modes in the Smith predictor and, hence, there is no additional hidden possibility to destabilize the system; (iii) it can be applied to systems with long dead-time without any difficulty. Hence, the practical significance is obvious.     

New delay-dependent non-fragile H∞ observer-based control for continuous time-delay systems

The problem of the delay-dependent non-fragile H_∞ observer-based control for a class of continuous time-delay systems is investigated in this paper. The additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain. Delay-dependent criteria are derived to guarantee the stability of the non-fragile H_∞ observer-based control system using the Lyapunov functional approach. The controller and observer gains are given from the LMI feasible solutions. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the non-fragile H_∞ observer-based controls. Computer software Matlab can be applied to solve all the proposed results. Finally, a numerical example is illustrated to show the improvement of this paper.     

An innovation approach to H∞ prediction for continuous-time systems with application to systems with delayed measurements

This paper studies the problem of H_∞ prediction for linear continuous-time systems. By developing a new method of characterizing the innovation process and applying a novel innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of a finite horizon H_∞ predictor is derived. The solution to the H_∞ prediction is given in terms of solutions of Riccati and matrix differential equations. We further extend our study to give a necessary and sufficient condition for the H_∞ filtering of linear continuous-time systems with both instantaneous and delayed measurements.     

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.     

A parametric optimization approach to H∞ and H2 strong stabilization

This paper presents an approach for designing stable MIMO H_∞ and H₂ controllers by directly computing the norm-constrained stable transfer matrices Q in the H_∞ and H₂ suboptimal controller parameterizations. This is done by first converting the H₂ and H_∞ strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parameterization of the norm-constrained Q's for any fixed order. Then, a two-stage numerical search is carried out by using a combination of a genetic algorithm and a quasi-Newton algorithm in order to reach an optimal solution. The effectiveness of the proposed algorithms is illustrated through some benchmark numerical examples.