基于LMI的不确定离散模糊时滞系统鲁棒控制

利用T-S模糊模型，讨论了一类具有状态时滞和控制输入时滞的不确定离散非线性系统鲁棒控制问题,基于Lyapunov稳定性理论，导出了系统采用线性矩阵不等式表示的时滞相关型鲁棒镇定充分条件，并设计了相应的状态反馈模糊控制器．仿真结果证明了所提出方法的有效性和可行性.     

含有输入时滞的不确定T-S模糊系统的滑模控制

研究同时包含输入时滞和状态时滞的不确定T-S模糊系统的滑模控制问题,其中非线性不确定项是未知的,并且不满足匹配条件.针对被控对象的T-S模糊模型,设计一种基于积分型切换面的滑模控制器,并利用线性矩阵不等式技术和李亚普诺夫稳定性理论,给出滑模动态渐近稳定的充分条件,设计滑模控制律使系统状态保持在切换面上.仿真结果表明,该方法能有效消除非线性不确定性和输入时滞给系统带来的影响.     

基于模糊模型的时滞不确定系统的模糊H∞鲁棒反馈控制

讨论了一类具有状态和控制时滞的不确定非线性系统的模糊H∞状态反馈控制问题.采用具有时滞的不确定Takagi-Sugeno(T-S)模糊模型对非线性系统进行建模,提出了一套基于LMI的模糊鲁棒控制器的系统设计方法,给出了模糊H∞状态反馈控制器存在的充分条件,以保证闭环模糊系统渐近稳定并满足从干扰输入到控制输出的H∞范数界约束.示例仿真表明了该方法的有效性.     

一类区间时变时滞T-S模糊系统的鲁棒控制

针对一类区同时变时滞T-S模糊系统,研究了其时滞相关渐近稳定性以及控制器设计问题.基于Lyapunov稳定性理论和线性矩阵不等式(LMI)工具,并结合自由权矩阵方法,设计一个包含时滞区间均值在内的新Lyapunov-Krasovskii泛函,给出了改进的时滞T-S模糊系统渐近稳定的时滞相关准则.同时,根据并行分布补偿算法,给出了带有记忆的状态反馈模糊控制器的设计方法.最后,实例仿真表明了方法的有效性.     

不确定时滞关联大系统的全局稳定模糊容错控制

研究了一类带有时变时滞的不确定非线性关联大系统的自适应模糊容错控制问题.用有界的参考信号代换模糊逼近器输入中的未知时滞信号,使得控制器的设计与应用不再依赖于时滞假设条件,使得控制器的设计和控制方法的应用更为方便.容错反推控制技术和自适应技术相结合来处理代换误差和逼近误差.所提出的方案能有效补偿所有4种类型的执行器故障,同时还可保证闭环系统的全局稳定性.仿真结果进一步验证了本文方法的有效性.     

前提不匹配的模糊时滞系统镇定条件的改进

本文研究了前提不匹配的Tagaki-Sugeno(T–S)模糊时滞系统的镇定问题.与一般的T–S模糊时滞系统相比,该系统中模糊模型与模糊控制器拥有不同的模糊规则数与不同的隶属度函数.基于Lyapunov稳定性理论,通过引进新型积分不等式,给出了包含隶属度函数信息的镇定条件.本文提出的新方法充分考虑了隶属度函数的信息,同时得到了Lyapunov函数导数的最小下界,因此新的镇定条件比以往结果具有更小的保守性.另一方面给出前提不匹配的控制器设计方法,由于模糊控制器的隶属度函数可以任意选取,因此提高了控制器设计的灵活性.最后仿真实例证明了本文方法的有效性及优越性.     

基于模糊模型的时滞不确定系统的模糊H∞鲁棒反馈控制

讨论了一类具有状态和控制时滞的不确定非线性系统的模糊H_∞ 状态反馈控制问题. 采用具有时滞的不确定Takagi-Sugeno(T-S)模糊模型对非线性系统进行建模, 提出了一套基于LMI的模糊鲁棒控制器的系统设计方法, 给出了模糊H_∞状态反馈控制器存在的充分条件, 以保证闭环模糊系统渐近稳定并满足从干扰输入到控制输出的H_∞范数界约束. 示例仿真表明了该方法的有效性.     

基于标度小增益定理的离散时滞模糊系统可靠H_∞控制

本文利用输入–输出方法,研究了带有时变时滞和执行器故障的离散T–S模糊系统可靠H∞控制问题,并使用一种更切合实际的离散齐次马尔可夫链来表示执行器故障的随机行为.首先,利用一类新的模型变换方法,将离散时滞T–S模糊系统转换为互联的两个子系统.然后,利用标度小增益定理分析互联子系统的随机稳定性.通过构造参数依赖的Lyapunov函数,给出闭环系统输入–输出均方稳定且满足H∞性能的充分条件及可靠H∞控制器的设计方法.最后,给出两个数值例子验证所提方法的有效性.     

一类切换模糊时滞系统的状态反馈控制

针对切换模糊时滞系统,根据平行分布补偿算法,设计了模糊状态反馈控制器.使用切换技术及单Lyapunov函数和多Lyapunov函数方法,给出了这一类切换模糊时滞系统渐近稳定的充分条件及切换律.仿真结果表明了方法的有效性.     

Global regulation of a class of feedforward and non-feedforward nonlinear systems with a delay in the input

In this paper, we propose a new state feedback controller using dynamic gain for input-delayed systems with high-order nonlinearity terms in both feedforward and non-feedforward forms. The controller design is based on a reduction method to remove the input delay and a gain scaling technique involving appropriate powers of high-order nonlinearity. As a result, more generalized systems containing feedforward and nonfeedforward terms with an input delay are regulated when the proposed power order condition of the nonlinear function is satisfied. An example is given to show the generality of our result over existing results.     

一类不确定广义时滞系统的弹性保性能控制

研究同时具有状态时滞和控制输入时滞的一类不确定广义系统的弹性保性能控制。基于线性矩阵不等式（LMI）方法,给出广义系统弹性保性能的充分必要条件及相应控制器的设计方法,数值例子验证该方法的可行性。     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Output feedback regulation of a class of high‐order feedforward nonlinear systems with unknown time‐varying delay in the input under measurement sensitivity

An output feedback regulation problem is considered for a class of high‐order feedforward nonlinear systems with delay in the input under measurement sensitivity. The key features are that the considered systems have uncertain high‐order feedforward nonlinearity and unknown time‐varying delay in the input. Then, the controller is supposed to be engaged where the output feedback information is distorted by measurement sensitivity. Our proposed controller has two gains—fixed and adaptive gains. The fixed gain is first designed to compensate for measurement sensitivity, and the adaptive gain is next utilized to dominate both unknown input delay and uncertain high‐order feedforward nonlinearity. Simulation examples are given to highlight the advantage of our control scheme.     

Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller     

利用提升-预估法设计离散时间时滞线性系统的预见控制器

研究一类既有状态时滞又有输入时滞的离散时间线性系统的预见控制问题.分别使用离散提升技术和变量替换法将系统中的状态时滞和输入时滞消掉,得到一个无时滞的系统.在此基础上,使用预见控制理论和状态预估法得到一个带有状态时滞补偿、输入时滞补偿和参考信号预见补偿的控制器.针对不同的时滞使用不同的方法进行消除,有效地降低了增广系统的维数.最后,通过一个数值算例验证了所提出设计方法的有效性.     

非线性时变时延系统的模糊采样最优控制

针对非线性时变时延系统,采用输入时延和自由权重矩阵方法研究模糊采样最优控制问题.应用T-S模糊系统表征非线性系统,控制器是零阶保持采样信号.由线性矩阵不等式给出最优控制准则,所设计的模糊采样控制器在闭环系统渐近稳定意义下可保证期望最优控制性能.最后,通过卡车拖车系统实验验证模糊采样控制设计方案的可行性.     

Robust delayed-state-feedback stabilization of uncertain stochastic systems

Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

Stabilization of Nonlinear Systems Under Variable Sampling: A Fuzzy Control Approach

This paper investigates the problem of stabilization for a Takagi-Sugeno (T-S) fuzzy system with nonuniform uncertain sampling. The sampling is not required to be periodic, and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound. By using the input delay approach, the T-S fuzzy system with variable uncertain sampling is transformed into a continuous-time T-S fuzzy system with a delay in the state. Though the resulting closed-loop state-delayed T-S fuzzy system takes a standard form, the existing results on delay T-S fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay. A new condition guaranteeing asymptotic stability of the closed-loop sampled-data system is derived by a Lyapunov approach plus the free weighting matrix technique. Based on this stability condition, two procedures for designing state-feedback control laws are given: one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints, which can be readily solved using standard numerical software. An illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology.