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.     

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.     

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.     

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.     

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H_∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H_∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.     

Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed T-S models

This work concerns the tracking problem of uncertain Takagi-Sugeno (T-S) continuous fuzzy model with external disturbances. The objective is to get a model reference based output feedback tracking control law. The control scheme is based on a PDC structure, a fuzzy observer and a H_∞ performance to attenuate the external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key point of the proposed approaches is to achieve conditions under a LMI (linear matrix inequalities) formulation in the case of an uncertain and disturbed T-S fuzzy model. This formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems. Finally, a simulation is provided on the well-known inverted pendulum testbed to show the efficiency of the proposed approach.     

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.     

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.     

基于T-S 模糊模型的网络控制系统非脆弱H∞ 跟踪控制

针对一类T-S 模糊模型描述的网络控制系统(NCSs) 非脆弱H_∞跟踪控制问题进行研究. 首先, 综合考虑网络中数据传输时滞和数据丢包的影响, 采用输入时滞法和并行分布补偿(PDC) 技术, 建立基于T-S 模糊模型的NCSs 状态跟踪误差模型; 然后, 利用Lyapunov 方法和改进的自由权矩阵方法, 基于线性矩阵不等式(LMI), 给出满足系统H_∞ 跟踪性能的条件, 并给出非脆弱模糊控制器设计方法; 最后, 通过仿真实例表明了该方法的有效性.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 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.     

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.     

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.