不确定广义时滞系统的鲁棒稳定方法研究

研究一类带有时滞不确定广义系统的鲁棒渐近稳定问题．利用Lyapunov稳定性定理和线性矩阵不等式工具,得到了广义系统正则、鲁棒渐近稳定的时滞相关充分条件．为了降低所得结果的保守性,避免了采用系统模型变换和利用矩阵不等式方法．进一步,建立一个具有线性矩阵不等式约束的凸优化问题,利用Matlab软件中的LMI工具箱求解,得到保证广义系统鲁棒渐近稳定的最大可允许时滞上界．仿真示例表明了该方法的有效性．     

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.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

线性离散时滞系统的鲁棒耗散控制

考虑线性离散时滞系统的二次型耗散控制问题.对于确定系统,给出渐近稳定且严格二次型耗散的条件和动态输出反馈控制器使闭环系统渐近稳定且严格二次型耗散.对于不确定系统,考虑不确定性具有耗散特性的情形,讨论鲁棒耗散性分析和动态输出反馈鲁棒耗散控制问题.通过构造增广系统,将不确定系统的鲁棒严格二次型耗散分析和设计转化为确定系统的情况.所得结果为离散时滞系统的无源控制和H∞控制提供了统一框架,且为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

时滞的不确定奇异摄动系统鲁棒稳定性研究

研究了带离散时滞和分布时滞的不确定奇异摄动系统的鲁棒稳定问题.首先采用广义系统模型方法,将所研究的系统转化为与之等价的广义系统;然后提出对应的Lyapunov-Krasovskii泛函,得到了时滞相关的鲁棒稳定性判据,并在此基础上给出了鲁棒控制器设计,结论以矩阵不等式形式给出;最后仿真算例说明了方法的有效性.     

不确定非线性时滞切换广义系统的鲁棒无源控制

将无源的概念从广义系统扩散到切换广义系统之中,进而研究了一类带有非线性扰动项和时滞不确定项的切换广义系统的无源控制问题。并且系统中的不确定性要满足有界条件。首先,基于一类广义Lyapunov函数结合线性矩阵不等式,获得了使非线性切换广义系统能够渐近稳定且严格无源的充分条件。然后,根据已给的条件设计出鲁棒无源控制器,使得闭环广义切换系统对于所有容许的不确定性是严格无源的。最后运用Matlab中的LMI工具箱具体给出实例,证明其可行性。     

不确定时滞离散非线性系统的鲁棒耗散滤波

研究了一类带参数不确定性和非线性动态的离散时滞系统的鲁棒耗散滤波问题.所给系统中的不确定项是时变未知且范数有界.基于Lyapunov稳定性方法,先对参数已知而带有非线性动态的时滞离散系统,给出渐近稳定判据,然后讨论鲁棒耗散滤波器的存在条件及设计方法.在此基础上进一步考虑参数不确定性情形,将鲁棒耗散滤波器问题转化为参数确定的情况.从而将鲁棒耗散滤波器的设计问题转换为线性矩阵不等式的求解问题.最后给出仿真例子验证所得结果的有效性.     

一类具有Markov跳跃参数的不确定混合线性时滞系统鲁棒稳定性研究

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒稳定性问题．分别给出了非匹配条件下不确定部分范数上界已知时使混合线性系统以概率1渐近稳定的充分条件,和匹配条件下不确定部分范数上界未知时同样可以实现混合系统以概率1渐近稳定的鲁棒自适应控制设计方案．文章研究结果表明,此控制方案对混合线性时滞系统的不确定部分是有效的．     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．     

线性不确定广义时滞系统的鲁棒无源滤波器设计

研究一类线性不确定广义时滞系统的鲁棒无源滤波器设计问题．系统中所含的不确定性假设是未知且范数有界的．利用线性矩阵不等式方法和Lyapunov函数方法相结合,给出了广义滤波增广系统时滞独立的鲁棒无源滤波器的存在条件．设计目标是对所有的不确定性,滤波增广系统是正则、稳定、无脉冲的,且满足所提的无源滤波性能指标．所提的滤波器设计问题可转化为标准的线性矩阵不等式的求解问题,并可推广到多时滞情况．数值例子验证了设计方法的可行性．     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closedloop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

离散广义系统的鲁棒严格正实控制

研究确定的以及具有范数有界不确定性的离散广义系统的严格正实分析和控制问题,首先给出了确定离散广义系统状态反馈扩展严格正实控制器的存在条件和设计方法;然后利用线性矩阵不等式分析了不确定离散广义系统广义二次稳定且扩展严格正实的条件,讨论了状态反馈使闭环系统广义二次稳定且扩展严格正实问题,给出了状态反馈鲁棒扩展严格正实控制器的综合方法;最后通过数值算例说明了所提出方法的有效性．     

离散奇异时滞系统时滞依赖稳定性分析与镇定

分别研究了离散奇异时滞系统时滞依赖稳定性分析与镇定问题. 首先给出了一个新的离散奇异时滞系统时滞依赖容许性充分条件. 经过证明, 所提出的方法与现有结论相比, 具有一定的优势. 然后, 运用矩阵理论技巧,设计出状态反馈控制器保证闭环离散奇异时滞系统是容许的. 最后,两个数值例子说明了所用方法的有效性.     

Robust H∞ Control of Uncertain Stochastic Systems with Time-varying Interval Delays

International Journal of Control, Automation and Systems - A robust delay-dependent stability criterion for discrete-time uncertain stochastic systems is proposed to achieve asymptotical stability...     

Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

Theoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.     

Stability and passivity analysis for Lur’e singular systems with Markovian switching

This paper is concerned with the stochastic stability and passivity analysis for a class of Lur’e singular systems with time-varying delay and Markovian switching. By using the free-weighting matrices approach, a delay-dependent stability criterion, which guarantees that the system is stochastically stable and robustly passive, is derived in terms of linear matrix inequality (LMI). Two numerical examples are provided to illustrate the effectiveness of the proposed method.     

Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.     

Robust stability analysis and stabilisation of uncertain neutral singular systems

This paper studies the problem of robust stability and stabilisation of uncertain neutral singular systems and develops a new stability criterion of the differential operator, ? by the final value theorem for Laplace transform. By utilising Lyapunov functional and free-weight matrix method, we employ the linear matrix inequality technique and the stability condition to derive some new criteria which ensure the robustly asymptotical stability of the studied system. State feedback controllers with disturbance are designed to guarantee the robustly asymptotical stability of the uncertain system. Numerical examples are provided to validate the effectiveness of the obtained results.     

Passivity-based decentralized stabilization of multi-agent systems with uncertainty and mixed delays

In this paper, we investigate a decentralized stabilization problem of uncertain multi-agent systems with mixed delays including discrete and distributed time-varying delays based on passivity stability. We design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent passivity stability for each subsystem. Then, by employing a new Lyapunov-Krasovskii function, a linear matrix inequality （LMI） approach is developed to establish the delay-dependent criteria for the passivity stability of multi-agent systems. The sufficient condition is given for checking the passivity stability. The proposed LMI result is computationally efficient. An example is given to show the effectiveness of the method.