Robust Stabilization of Delayed Systems with Rank-1 Type Uncertainties

This paper deals with the problem of robust stabilizationfor the systems with rank-1 type uncertainties and mul-tiple state delay.Firstly,a new delay-dependent crite-ria is presented for unforced normal delayed system to bestable.Based on the obtained criteria,a new LMI ap-proach is developed for robust stabilization of a class ofuncertain delay systems via linear memoryless state feed-back control law.The results depend on the size of thedelays and are given in terms of linear matrix inequali-ties.And so no tuning procedure for scalars and/or ma-trices is required and the results are less conservativethan those of delay-independent.Finally,an illustra-tive example is presented.     

Robust H_∞ Control of Uncertain Linear Systems with Multiple State Delays—LMI Approach

This paper deals with the problem of robust H∞ control for uncertain systems with multiple state delays. The parameter uncertainties are unknown but norm - bounded. An LMI based method is developed for robust H∞ stabilization for a class of uncertain systems with multiple state delays via linear memoryless state feedback control. The resuits depend on the size of the delays and are given in terms of linear matrix inequalities, so they are less con. servative than those of delay - independent.     

Fault-Tolerant Control for a Class of Uncertain Systems with Actuator Faults

The problem of fault-tolerant controller design for a class of polytopic uncertain systems with actuator faults is studied in this paper. The actuator faults are presented as a more general and practical continuous fault model. Based on the affine quadratic stability (AQS), the stability of the polytopic uncertain system is replaced by the stability at all corners of the polytope. For a wide range of problems including H∞ and mixed H 2 /H∞ controller design, sufficient conditions are derived to guarantee the robust stability and performance of the closed-loop system in both normal and fault cases. In the framework of the linear matrix inequality (LMI) method, an iterative algorithm is developed to reduce conservativeness of the design procedure. The effectiveness of the proposed design is shown through a flight control example.     

Robust Controller Design of a Class of Uncertain Switched Fuzzy Systems with Delays

The robust control problem for a class of uncertain switched fuzzy systems with delays is investigated. Firstly,the model of the switched fuzzy system is presented and the parallel distributed compensation（ PDC） technology is employed to design fuzzy controllers. Then, based on the convex combination method, a sufficient condition for robust stabilization in terms of linear matrix inequalities（ LMIs） is obtained and a switching law is presented.Meanwhile,the Lyapunov-Krasovskii functional is taken to deal with time varying delays. Moreover,an algorithm is applied to finding a solution for a group of convex combination coefficient. Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.     

Robust stabilization of multilinear interval plants

The robust D-stability of a class of multilinear interval polynomials is considered. Some sufficient conditions are given to judge the robust D-stability of the uncertain systems. In short, an uncertain system is robustly D-stable if some linear matrix inequalities are solvable. Moreover, our results are applied to the robust stabilization of multilinear interval plants. Taking advantage of the uncertainty structure information, these results are computationally tractable and effective in practice.     

Robust control for uncertain singular systems with time-varying delay

We study the problem of L2-L∞, control for a class of uncertain singular systems with time-delay and norm-bounded parameter uncer- tainties in this paper. A new delay-dependent robust stability criterion is obtained in terms of linear matrix inequalities （LMIs）. Based on this criterion, a state feedback controller is designed to guarantee that the closed-loop system is regular, impulse free and stable with a prescribed L2-L∞ performance satisfied for all admissible parameter uncertainties. A simulation example is included to illustrate the effectiveness of the proposed method.     

H∞ control for uncertain Markovian jump systems with mode-dependent mixed delays

We study the problem of H∞ control for a class of Markovian jump systems with norm-bounded parameter uncertainties and mode-dependent mixed delays including discrete delays and distributed delays in this paper. Our aim is to present a new delay-dependent control approach such that the resulting closed-loop system is robust mean-square （MS） exponentially stable and satisfies a prescribed H∞ performance level, irrespective of the parameter uncertainties. Such delay-dependent approach does not require system transformation or free-weighting matrix. A numerical example shows that the results are less conservative and more effective.     

Robust Stabilization for Uncertain Linear Delay Markow Jump System

Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with uncertainty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.     

LMI-based delay-dependent robust control for value bounded uncertain systems with time delay

The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding “zeros” matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality (LMI). LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.      

不确定中立变时滞系统的鲁棒H∞控制

研究了一类不确定中立变时滞系统的鲁棒比控制问题．时滞假定为未知并且时变．基于Lyapunov-Krasovskii范函理论,提出了状态反馈控制器存在的时滞依赖判据,保证了系统是鲁棒镇定并且满足噪声衰减律．采用了线性矩阵不等式（LMI）方法解决鲁棒巩控制问题．最后,给出了一个算例证明了该结论是可行的．     

不确定关联时滞大系统的分散鲁棒稳定控制器设计

对一类具有数值界不确定性关联时滞大系统,应用线性矩阵不等式(LMI)方法研究使其分散稳定化的鲁棒控制器设计问题.给出了其存在分散鲁棒稳定化控制器的充分条件,在此基础上,通过求解一凸优化问题,指出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法.仿真示例说明了该方法的应用.     

一类带有扰动的不确定切换系统的鲁棒镇定

研究了一类带有非线性扰动的不确定切换系统的鲁棒镇定问题．利用完备性条件，得到了不确定切换系统渐近稳定的一个充分条件．基于LMI方法，设计出鲁棒状态反馈控制器及相应的切换策略，使得闭环系统在其平衡点处是渐近稳定的．     

不确定多时滞广义系统的鲁棒控制器设计

研究了针对一类不确定性多时滞广义系统的鲁棒控制问题,系统的奇异矩阵满足一定假设条件的。提出了一种基于线性矩阵不等式(LMI)的鲁棒控制器的设计方法,并证明了该鲁棒控制器可以保证原系统与其组成的闭环系统是全局一致指数稳定的。该控制器既消除了多时滞所带来的不良影响,又使系统具有很强的鲁棒稳定性,设计方法简单,求解容易。通过一个数值算例,说明了所给方法的有效性。     

基于LMI的不确定大系统的BIBO镇定

利用多Lyapunov函数法和不等式技巧,讨论了一类连续时间大系统有界输入有界输出(BIBO)的镇定.以线性矩阵不等式(LMI)的形式给出系统BIBO稳定的充分条件可以用MATLAB工具箱进行可行性求解并在此基础上给出了状态反馈控制器的设计方法并将其推广到系统结构中存在不确定扰动项的情形,运用Schur补引理,得到了闭环大系统鲁棒BIBO稳定的判据.最后通过算例仿真证明了结论的有效性.     

一类不确定脉冲时滞系统的指数镇定

针对一类不确定脉冲时滞系统的鲁棒控制问题,通过设计鲁棒状态反馈控制器以消除脉冲扰动和时滞对系统的影响,从而使系统稳定.为此基于Lyapunov稳定性理论,选取适当的Lyapunov函数并结合Riccati方程以及线性矩阵不等式技术,设计状态反馈控制器,使得闭环系统实现鲁棒指数稳定.通过求解线性矩阵不等式给出鲁棒控制器的设计方法,最后通过数值例子说明方法的有效性.     

圆盘区域极点约束鲁棒非脆弱控制

针对一类参数不确定线性系统,研究了具有圆盘区域极点约束的状态反馈鲁棒非脆弱控制器设计问题。系统中的参数不确定性满足范数有界条件,设计的非脆弱控制器具有加性和乘性不确定项。基于线性矩阵不等式(LMI),提出了将闭环系统极点配置到指定圆盘区域的状态反馈鲁棒非脆弱控制器存在的充分条件。然后利用G辅助变量替换技术拓展了圆盘极点配置的线性矩阵不等式(LMI)条件,提出保守度较低的状态反馈非脆弱控制器设计方法。数值仿真例子验证了给出的控制器设计方法的可行性。     

随机马尔可夫跳跃系统的输出反馈镇定

针对不确定随机马尔可夫跳跃系统,研究其静态输出反馈控制问题.目的在于寻找输出反馈控制器使得闭环系统均方稳定.通过Lyapunov函数方法以矩阵不等式形式建立了这类系统输出反馈可镇定的充分条件;采用替换LMI(linear matrix inequality)方法给出了这些非线性矩阵不等式的一种解法,并给出了静态反馈控制律的求解算法.仿真算例说明所给方法的有效性.