不确定广义跳变时滞系统的鲁棒指数稳定性

讨论不确定广义跳变时滞系统的鲁棒指数稳定性问题. 利用线性矩阵不等式(LMI)技术给出一个时滞区间依赖条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 数值例子说明本文的结果改进了已有的结论.     

一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.     

不确定广义时滞系统的时滞依赖鲁棒H∞控制

讨论不确定广义时滞系统的时滞依赖鲁棒H∞控制问题. 基于线性矩阵不等式(LMI)方法, 设计状态反馈控制器使得对所有允许的不确定性, 所得的闭环系统均是正则、无脉冲、稳定且满足H∞范数有界约束. 所有的结论都是时滞依赖的且由不涉及系统矩阵分解的严格LMI表示. 数值例子表明所给的方法与已有的结论相比具有较小的保守性.     

时滞相关型离散时变时滞奇异系统的鲁棒镇定

讨论含参数不确定的离散时变时滞奇异系统的时滞相关的鲁棒状态反馈稳定化问题. 在一系列等价变换下, 阐述了其和一个不确定正常线性离散时变时滞系统的鲁棒状态反馈稳定化问题的等价关系;利用矩阵不等式方法, 给出一个对所有容许的不确定, 使得闭环系统正则、因果且稳定的时滞相关鲁棒状态反馈稳定化控制器存在的充分条件以及无记忆状态反馈控制器的一个解.     

具有数据包丢失的奇异网络控制系统指数稳定性

考虑存在时延和数据包丢失的情况,研究了奇异被控对象的网络控制系统建模与指数稳定性问题.当时延不大于一个采样周期且数据包丢失率一定时,将正则、无脉冲的奇异网络控制系统建模为数据包丢失率约束的异步动态切换系统,给出了状态反馈和动态输出反馈的统一数学模型;推导出数据包丢失率约束的系统指数稳定的充分条件,给出了使系统指数稳定的最大允许数据包丢失率,仿真结果表明了该方法的有效性和可行性.     

基于T-S模糊模型的多时滞非线性网络切换控制系统非脆弱H∞控制

针对一类控制器增益存在摄动的不确定非线性网络切换系统,在系统同时存在随机时变时滞和数据包丢失的情况下,研究系统的非脆弱H_∞控制问题.首先,利用T-S模型,将非线性网络切换系统建模为网络切换模糊系统;其次,将数据包丢失作为时滞处理,并采用Bernoulli分布的随机序列描述该时滞;再次,采用平均驻留时间的方法(ADT)设计系统的切换律及非脆弱状态反馈控制器,并给出网络切换模糊时滞系统指数稳定的平均驻留时间条件;最后,结合李雅普诺夫(LKF)方法给出系统均方指数稳定且满足H_∞性能指标的充分条件.仿真结果验证了所提出设计方法的有效性.     

广义时滞系统时滞依赖H∞控制的改进结果

讨论广义时滞系统的时滞依赖控制问题. 基于线性矩阵不等式(LMI)方法和增广Lyapunov泛函, 给出保证系统正则、无脉冲、稳定且满足性能指标的时滞依赖有界实引理. 在此引理的基础上, 给出基于严格LMI的状态反馈控制器存在的时滞依赖条件. 同时给出所需状态反馈控制器的明确表示. 数值例子表明本文的结果改进了已有结论的保守性.     

非相称多时滞奇异系统的有记忆状态反馈控制

针对一类非相称多时滞奇异系统, 研究其时滞相关稳定性问题. 给出了易于数值检验的时滞无关正则条件. 基于Lyapunov-Krasovskii泛函方法和广义积分引理给出了系统时滞相关稳定的充分条件. 本文的主要思想是利用矩阵不等式方法, 设计有记忆状态反馈控制器, 使相应的闭环系统时滞无关正则、无脉冲、渐进稳定, 并直接给出了有记忆状态反馈控制器参数化的表达形式. 最后通过数值仿真验证了所提方法的有效性.     

一类时滞奇异系统的H ∞鲁棒控制

讨论一类具有状态及输入时滞的线性奇异系统的H^∞鲁棒控制问题，利用线性矩阵不等式(LMI)方法，给出一个使闭环系统正则、无脉冲模、稳定，且满足H^∞鲁棒性能指标的状态反馈控制器存在的充分条件，同时给出了一类奇异系统可鲁棒镇定的充要条件。     

具有数据包丢失的奇异网络控制系统指数稳定性

考虑存在时延和数据包丢失的情况,研究了奇异被控对象的网络控制系统建模与指数稳定性问题.当时延不大于一个采样周期且数据包丢失率一定时,将正则,无脉冲的奇异网络控制系统建模为数据包丢失率约束的异步动态切换系统,给出了状态反馈和动态输出反馈的统一数学模型,推导出数据包丢失率约束的系统指数稳定的充分条件,给出了使系统指数稳定的最大允许数据包丢失率.仿真结果表明了该方法的有效性和可行性.

     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities (LMIs) involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems

In this note, the delay-dependent robust stability criteria for two classes of singular time-delay systems with norm-bounded uncertainties are investigated. First, without using model transformation and bounding technique for cross terms, an improved delay-dependent stability criterion for the nominal singular time-delay system is established in terms of strict linear matrix inequalities (LMIs). Then, based on this criterion, the delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems are proposed, which ensure that the systems are regular, impulse free and asymptotically stable for all admissible uncertainties. Numerical examples are proposed to illustrate the less conservatism of the obtained results     

一类不确定Lurie时滞奇异系统的鲁棒H∞滤波

This paper deals with the problem of the robust H∞ filtering for a class of Lurie singular systems with state time-delays,parameter uncertainties and unknown statistics characteristics but with limited power disturbance, aiming to design a robustly stable filter such that the uncertain Lurie time-delay singular systems are not only regular, impulse free and stable, but also have 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 linear matrix inequalities (LMIs). When a solution to this set of LMIs exists, the parametric matrices of a desired filter can be easily obtained using LMI toolbox.     

Robust stability of uncertain singular time-delay systems via LFT approach

The robust stability problem of continuous-time singular systems with multiple state delays and bounded parametric uncertainties is considered. Both commensurate and non-commensurate delays are investigated. On the basis of the linear fractional transformations (LFTs) framework and μ-analysis, a systematic approach is derived to convert the robustness problem to a robust nonsingularity problem. Some explicit conditions are proposed to guarantee the uncertain singular time-delay system being regular, impulse-free and stable independent of delay. Two illustrative examples are given to show the feasibility of the proposed technique.     

Dissipative control for singular time-delay system with actuator saturation via state feedback and output feedback

This paper is devoted to the problem of dissipative control for a class of singular time-delay systems with actuator saturation via state feedback and output feedback. First, by tuning the Wirtinger-based integral and the double integral inequality, a sufficient condition is derived to guarantee that the singular time-delay system is regular, impulse free, asymptotically stable and strictly (Q,S,R)-dissipative. Then, based on the derived condition, and applying linear matrix inequality techniques, the dissipative state feedback and output feedback controller are synthesised. Moreover, the maximal estimate of the domain of attraction is proposed by an optimisation problem. Finally, some simulation examples are provided to verify the effectiveness of the obtained theoretic results.     

广义系统的时滞依赖静态输出反馈控制

针对一类不确定线性广义时滞系统,给出了静态输出反馈控制器的设计方法.首先基于标称广义时滞系统的稳定条件,以受限线性矩阵不等式形式,给出闭环广义时滞系统正则、无脉冲且渐近稳定的充分条件,同时利用受限矩阵不等式的可行解给出静态输出反馈控制律的一个参数化表示;其次,利用矩阵的正交补,把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式(LMIs)的可行解;最后应用数值实例说明了所给方法的有效性和正确性.     

Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation

This note considers the generalized quadratic stability problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples.