一类非线性滞后广义系统解的基本理论

本文讨论了一类指标大于１的非线性滞后广义系统,得到了其初值问题解的存在唯一性的结果,这些结果也适用于指标为１的滞后广义系统     

滞后广义系统状态跟踪的学习控制算法

尝试性的将迭代学习控制方法应用于滞后广义系统的状态跟踪控制上,针对满足Ａ２２可逆条件的滞后广义系统,给出了跟踪控制的学习算法,并对算法的收敛性及状态跟踪的可能性进行了分析。我们所设计的学习控制器对系统有很好的鲁棒性能,对Ａ２２不可逆,对此将另文讨论。     

Boundary Value Problems for Singular and Time-delay Measure Differential Systems with Impulsive Effects

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A singular bioeconomic model with diffusion and time delay

This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena: Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.     

区间时滞相关不确定奇异系统的鲁棒稳定性和镇定性

研究区间时滞相关的不确定时变时滞奇异系统的鲁棒稳定性和镇定性问题,不确定参数假设是范数有界的。充分利用时滞的下界信息构造Lyapunov函数,用严格的矩阵不等式给出系统对所有的容许不确定满足正则、无脉冲、稳定的新判据。基于这个判据,设计状态反馈控制器使得系统鲁棒稳定。数值例子说明所得结果具有更小的保守性。     

有包丢失的动态输出反馈奇异网络化系统稳定性分析

基于正则、无脉冲的奇异被控对象,研究了同时具有时延和数据包丢失的动态输出反馈网络控制系统的建模和稳定性问题。 当时延不大于一个采样周期、数据包丢失率一定时,将动态输出反馈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,利用切换系统和线性矩阵不等式方法,推导出数据包丢失率约束的系统指数稳定的充分条件,并且给出了系统指数稳定的指数衰减率以及最大容许数据包丢失率。仿真实验说明分析方法和研究结果是有效可行的。     

Stability of singular networked control systems with control constraint

Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.     

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvab...     

奇异不确定性多时滞系统的二次稳定性与H∞控制

针对奇异不确定性多时滞系统,研究了其二次稳定性及H∞状态反馈控制器的设计.假定其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了其二次稳定性及H∞状态反馈控制器存在的条件.仅通过求解相应的线性矩阵不等式(linear matrix inequality,LMI)就可得到鲁棒H∞控制器,设计的控制器对所有容许的不确定性不仅使得相应的闭环系统渐进稳定,也能保证闭环系统满足一定的H∞性能指标,达到抑制干扰的效果.最后,用数值算例及仿真验证了所给方法的有效性.     

Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems

The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.     

Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems

The problem of robust stabilization for uncertain singular time-delay systems is studied. First, a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given, which is less conservative. Using this result, the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed, Finally, two examples are given to illustrate the effectiveness of the results.     

Stability of discontinuous nonlinear singular systems

This paper studies a class of nonlinear singular systems with discontinuous right-hand sides, it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle. In this paper, LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly. Furthermore, some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke’s generalized gradient are given. Finally, these results are illustrated by the given example.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Consensus and r-consensus problems for singular systems

In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, linear systems with algebraic constraints are considered, and the corresponding results about consensus and average-consensus are derived. Then r-consensus and consensus problems of singular systems are investigated. Sufficient conditions of r-consensus and consensus are obtained, respectively. Finally, an illustrative example is given to show the effectiveness of the proposed method.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.     

滞后广义系统的渐近稳定与镇定

广义系统的渐近稳定与镇定问题是广义系统理论的基本问题之一,在许多领域均有应用,时滞广义系统的研究与无时滞广义系统相比要困难得多。利用广义Lyapunov泛函方法研究了具滞后的广义系统的渐近稳定性和镇定问题,给出了渐近稳定判定定理,设计了适当的反馈律,以实现滞后广义系统的镇定,方法简单,直观,易于理解,给出的例子说明了该定理的可行性。     

滞后广义系统的变结构控制

运用变结构控制方法,研究了控制具滞后和控制不具滞后的滞后广义系统,对这两类滞后广义系统,利用滞后积分来选取切换流形,设计变结构控制率.分析了切换流形上其滑动模态区的存在性.利用广义Lyapunov泛函分析了其闭环系统的稳定性,给出了其闭环系统渐近稳定的充分条件.为了说明文中定理的可行性,给出了一个数值实例.通过该例子,可看出其变结构控制器设计与无滞后的广义系统和古典系统的变结构控制器的设计不同.     

改进的SVD算法对BOC信号组合码与信息序列盲估计

针对低信噪比下二进制偏移载波信号的组合码序列以及信息序列盲估计问题,在未知时延下,利用奇异值分解(singular value decomposition,SVD)算法估计出的组合码序列及信息序列,其最大奇异向量和次大奇异向量之间可能存在酉模糊现象。对于该问题的研究,提出一种改进的SVD方法对最大奇异向量及次大奇异向量进行线性组合,接着最优化筛选出其相应的系数矩阵,最后结合系数矩阵估计出组合码序列与信息序列。仿真结果表明,改进的SVD算法可同时应用于组合码和信息序列的估计且不受未知时延的影响,具有消模糊效果好、需要数据量少和抗噪性能强的特点。     

具有无界时变时滞的线性系统的稳定性

讨论了一类无界时变时滞线性系统的稳定性，给出了无界时变时滞线性系统稳定性的充分条件，这些条件也适用于常时滞系统。同时讨论了具有多个无界时变时滞系统的稳定性，并且改进了一些已有的关于常时滞系统稳定性的结论。最后给出了本文结论的两个示例。