A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design 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.     

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∞ 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.     

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.     

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.     

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.     

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.     

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.     

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.     

Reduced-order controllers for the H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H_∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H_∞ control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H_∞ control problems.     

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.     

不确定多智能体互联动态系统分布式鲁棒H∞协同控制

研究一类具有时延和切换拓扑的不确定多智能体互联系统的分布式协同控制问题,提出一类分布式鲁棒H∞协同控制器.该控制器能够在满足期望的H∞性能指标的前提下,使得所有智能体鲁棒地跟踪虚拟Leader.针对所提出的分布式H∞协同控制器,借助Lyapunov-Krasovskii泛函,利用线性矩阵不等式,推导出一系列充分(必要)条件,并且在通信拓扑连通的前提条件下,给出整个闭环系统的稳定性证明.仿真实例表明了所提出方法的有效性.     

Use of integrator in nonlinear H∞ design for disturbance rejection

The disturbance suppression problem for nonlinear systems is examined in this paper. We review the so-called nonstandard mixed sensitivity problem, which introduces an integrator to a selected weight, as well as the linear classical disturbance suppression problem and the linear H_∞ disturbance suppression problem. We extend this H_∞ problem to the nonlinear case, and present a method to reduce the order of the state feedback Hamilton-Jacobi (HJ) partial differential equation for this nonlinear H_∞ problem by extending the concept of comprehensive stability (Proceedings of the 36th Conference on Decision and Control, 1997, p. 4653; IEEE Trans. Ind. Electron. (1998) 488). Finally, we investigate the structure of the output feedback H_∞ controller for disturbance suppression, and draw the conclusion that, as in the linear case, there must also be an integrator in the controller.     

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.     

Synthesis of H∞ PID controllers: A parametric approach

This paper considers the problem of synthesizing proportional-integral-derivative (PID) controllers for which the closed-loop system is internally stable and the H_∞-norm of a related transfer function is less than a prescribed level for a given single-input single-output plant. It is shown that the problem to be solved can be translated into simultaneous stabilization of the closed-loop characteristic polynomial and a family of complex polynomials. It calls for a generalization of the Hermite-Biehler theorem applicable to complex polynomials. It is shown that the earlier PID stabilization results are a special case of the results developed here. Then a linear programming characterization of all admissible H_∞ PID controllers for a given plant is obtained. This characterization besides being computationally efficient reveals important structural properties of H_∞ PID controllers. For example, it is shown that for a fixed proportional gain, the set of admissible integral and derivative gains lie in a union of convex sets.     

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.     

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.

     

H∞ filtering of networked discrete-time systems with random packet losses

This paper studies the H_∞ filtering problem for networked discrete-time systems with random packet losses. The general multiple-input-multiple-output (MIMO) filtering system is considered. The multiple measurements are transmitted to the remote filter via distinct communication channels, and each measurement loss process is described by a two-state Markov chain. Both the mode-independent and the mode-dependent filters are considered, and the resulting filtering error system is modelled as a discrete-time Markovian system with multiple modes. A necessary and sufficient condition is derived for the filtering error system to be mean-square exponentially stable and achieve a prescribed H_∞ noise attenuation performance. The obtained condition implicitly establishes a relation between the packet loss probability and two parameters, namely, the exponential decay rate of the filtering error system and the H_∞ noise attenuation level. A convex optimization problem is formulated to design the desired filters with minimized H_∞ noise attenuation level bound. Finally, an illustrative example is given to show the effectiveness of the proposed results.     

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.