一类含未建模动态的奇异时滞系统的鲁棒镇定问题

利用线性矩阵不等式的方法，研究了一类同时含有参数摄动和未建模动态的线性奇异时滞系统的鲁棒镇定问题.得到了系统可鲁棒镇定的一个充分条件，用线性矩阵不等式的方法，将控制器的求解问题转化为受限线性矩阵不等式的求解问题，并给出了受限线性矩阵不等式的具体解法．最后举例说明了所提出方法的正确性．     

时滞模糊奇异摄动系统的H2次优控制

引入了时滞模糊奇异摄动模型.这里模糊规则后件为线性时滞奇异摄动模型,整个系统的动力学由各规则后件的线性动力学通过隶属函数插值得到,从而形成一类非线性时滞奇异摄动系统.系统的稳定性分析和H₂控制器设计方法可以归结为求解一组线性矩阵不等式,该组条件与小参数无关,故较好地回避了数值求解的病态问题.最后给出了仿真实例.     

不确定广义系统的弹性H∞保性能控制

利用线性矩阵不等式(LMI)方法,研究被控对象与控制器同时存在摄动的H∞保性能控制问题.针对控制器存在加法式摄动情形,以线性矩阵不等式约束条件给出了广义系统弹性H∞保性能的充分条件,并以线性矩阵不等式的可行解给出了相应的控制器设计方法.通过求解具有线性矩阵不等式约束的凸优化问题,给出了弹性H∞最优保性能及最优H∞性能控制器的设计方法.仿真表明了方法的可行性.     

基于迭代线性矩阵不等式的奇异摄动系统同时镇定

研究了采用一个线性状态反馈控制器镇定多个线性奇异摄动系统的问题.同时镇定条 件可以表达为一组矩阵不等式条件,所得条件与摄动参数无关,从而有效地回避了病态问题.采 用基于快慢分解的两步法可以得到镇定控制器增益和相应的Lyapunov函数.而在每一步需要利 用迭代线性矩阵不等式技术求解相应的双线性矩阵不等式,相关定理研究了算法的收敛性.本文 所得结论可同时适用于标准与非标准奇异摄动系统.文末给出了相应的仿真算例.     

模糊系统H∞控制器设计的LMI方法

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统H∞控制器的设计问题.首先给出了T-S模糊系统基于状态反馈H∞控制存在的两个新的充分条件.新条件不但简洁而且把模糊子系统间的相互作用表示为由子系统的系数矩阵构成的矩阵不等式.然后新条件被转化为可直接应用Matlab求解的线性矩阵不等式.最后应用线性矩阵不等式方法和Matlab,给出了T-S模糊系统H∞控制器的设计方法.     

模糊奇异摄动系统H∞滤波

针对一类非线性奇异摄动系统,建立基于T-S模糊模型的模糊奇异摄动系统模型,通过Lyapunov方法和Schur补定理,研究其H∞滤波问题.将系统H∞滤波器设计归结为求解一组与摄动参数ε无关的线性矩阵不等式,从而避免由ε引起数值求解的病态问题.所获得的滤波器使闭环系统渐近稳定并能达到给定的H∞性能指标.该方法适用于标准和非标准非线性奇异摄动系统,仿真实例表明了所提出方法的有效性.     

模糊系统H∞控制器设计的LMI方法

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统H_∞控制器的设计问题.首先给出了T-S模糊系统基于状态反馈H_∞控制存在的两个新的充分条件.新条件不但简洁而且把模糊子系统间的相互作用表示为由子系统的系数矩阵构成的矩阵不等式.然后新条件被转化为可直接应用Matlab求解的线性矩阵不等式.最后应用线性矩阵不等式方法和Matlab,给出了T-S模糊系统H_∞控制器的设计方法.     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

基于T-S模型的非线性时滞系统非脆弱保性能模糊控制

针对一类用T-S模糊模型描述的非线性时滞系统,采用状态反馈的并行分布补偿方法,研究其保守性较小的非脆弱保性能模糊控制问题,使闭环系统在控制器存在加性摄动的情况下,其闭环性能指标值低于确定的上界.利用线性矩阵不等式处理方法,导出了非脆弱保性能模糊控制律的存在条件,通过建立和求解一个线性矩阵不等式问题,给出了非脆弱保性能模糊控制律的设计方法.仿真结果表明了所提出方法的有效性.     

不确定广义系统的弹性H∞保性能控制

利用线性矩阵不等式（LMI）方法，研究被控对象与控制器同时存在摄动的H∞保性能控制问题。针对控制器存在加法式摄动情形，以线性矩阵不等式约束条件给出了广义系统弹性H∞保性能的充分条件，并以线性矩阵不等式的可行解给出了相应的控制器设计方法。通过求解具有线性矩阵不等式约束的凸优化问题，给出了弹性H∞最优保性能及最优H∞性能控制器的设计方法。仿真表明了方法的可行性。     

Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems

This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H^infin control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all epsivisin(0,epsiv^*) and the allowable perturbation bound epsiv^* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme     

Hinfinity fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: an LMI approach.

This paper considers the problem of designing an H infinity fuzzy controller with pole placement constraints for a class of nonlinear singularly perturbed systems. Based on a linear matrix inequality (LMI) approach, we develop an H infinity fuzzy controller that guarantees 1) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and 2) the closed-loop poles of each local system to be within a pre-specified LMI stability region. In order to alleviate the ill-conditioned LMIs resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation, epsilon. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard singularly perturbed non-linear systems. A numerical example is provided to illustrate the design developed in this paper.     

Fuzzy H/sub /spl infin// output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach

This paper examines the problem of designing an H/sub /spl infin// output feedback controller with pole placement constraints for singular perturbed Takagi-Sugeno (TS) fuzzy models. We propose a fuzzy H/sub /spl infin// output feedback controller that not only guarantees the /spl Lscr//sub 2/-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, but also ensures closed-loop poles of each subsystem are in a prespecified linear matrix inequality (LMI) region. In order to alleviate the numerical stiffness caused by the singular perturbation /spl epsiv/, the design technique is formulated in terms of a family of /spl epsiv/-independent linear matrix inequalities. The proposed approach can be applied both standard and nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

基于部分状态信息的模糊控制器设计

基于部分状态信息的控制器是一类特殊的静态输出反馈控制器,一般难以利用线性 矩阵不等式工具求解.该文研究了Takagi-Sugeno模糊模型的部分状态反馈控制问题,设计问 题可以归结为求解一组双线性矩阵不等式.通过使控制器增益由全状态反馈变化为部分状态 反馈,这类双线性矩阵不等式可以利用同伦算法求解.从而,镇定模糊部分状态反馈控制器可 以通过迭代方法得到.仿真例子验证了算法的有效性.     

A new result on state feedback robust stabilization for discrete‐time fuzzy singularly perturbed systems

This paper presents the novel results for stabilizing uncertain standard discrete‐time fuzzy singularly perturbed systems (SPSs) via a state feedback control law. Two standard discrete‐time fuzzy SPSs are constructed firstly by using the Takagi‐Sugeno (T‐S) fuzzy model. Based on a matrix spectral norm approach, two new ε‐dependent stability conditions are derived, which guarantee the resulting closed‐loop systems are asymptotically stable. The gains of controllers are obtained by solving a set of ε‐dependent linear matrix inequalities (LMIs). In contrast to the existing results, the proposed methods have two advantages: (i) the designed controllers can overcome the external disturbances and parameter uncertainty; and (ii) the upper bound of ε is improved, especially it is not required to be smaller than one. Examples are provided to illustrate the reduced conservatism of our results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Actuator fault tolerance based on continuous-time fuzzy singularly perturbed model

Actuator fault tolerance based on fuzzy singularly perturbed model (FSPM) for nonlinear singularly perturbed systems (NSPSs) is investigated. A continuous-time FSPM with subtractive faults on control input is presented to describe NSPSs with actuator faults, which is less conservative than slow–fast submodel methods. A hybrid fuzzy controller (HFC) consisting of a fuzzy detector and a fault-tolerant controller can realize real-time fault tolerance, such that the target system with actuator faults is stabilized. The theorem to solve controller gains is derived by using Lyapunov, singular perturbation, $H_{\infty }$, and Schur complement theories, which can avoid the problem that the feasible solutions cannot be obtained by solving linear matrix inequalities (LMIs). A nonlinear item was replaced by a linear item, which provides a good idea for solving nonlinear matrix inequalities. The sudden and remittent actuator faults of a motor system are suppressed by using the above approaches.     

Stability analysis and synthesis of fuzzy singularly perturbed systems

In this paper, we investigate the stability analysis and synthesis problems for both continuous-time and discrete-time fuzzy singularly perturbed systems. For continuous-time case, both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities (LMIs). For discrete-time case, only the analysis problem can be cast in LMIs, while the derived stability conditions for controller design are nonlinear matrix inequalities (NMIs). Furthermore, a two-stage algorithm based on LMI and iterative LMI (ILMI) techniques is developed to solve the resulting NMIs and the stabilizing feedback controller gains can be obtained. For both continuous-time and discrete-time cases, the reduced-control law, which is only dependent on the slow variables, is also discussed. Finally, an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures.     

New results on static output feedback H ∞ control for fuzzy singularly perturbed systems: a linear matrix inequality approach

This paper presents the novel approaches of designing robust fuzzy static output feedback H _∞ controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H _∞ controllers. The resulted controllers can guarantee that the closed‐loop systems are asymptotically stable and satisfy H _∞ performances for sufficiently small ?. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ?‐independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust Control of Uncertain Markov Jump Singularly Perturbed Systems

In this paper,we study the robust control for uncertain Markov jump linear singularly perturbed systems(MJLSPS),whose transition probability matrix is unknown.An improved heuris- tic algorithm is proposed to solve the nonlinear matrix inequalities.The results of this paper can apply not only to standard,but also to nonstandard MJLSPS.Moreover,the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical prob- lems.