随机时变时滞马尔可夫跳变系统的镇定研究

研究了一类转移概率部分未知的随机时变时滞马尔可夫跳变系统的鲁棒H∞控制问题.首先,构建Lyapunov-Krasovkii方法,设计无记忆的状态反馈控制器,保证闭环系统的随机稳定性.其次,将过程转化为求解一组线性矩阵不等式(linear matrix inequalities,LMIs)的约束优化问题,通过求解线性矩阵不等式的方式,获得了充分条件.最后,数值仿真验证结论的有效性.     

含非线性和马尔可夫跳变随机延时系统的延时相关指数稳定性

本文分析了一类含非线性和马尔可夫跳变随机延时系统的均方指数问题.通过改进文献[3]中的方法,得到了一个新的延时相关指数稳定性判据,且该判据可被描述为线性矩阵不等式的形式.数值实例证实了该稳定性判据的优越性,并提高了已有结果关于最大允许延时的估计.     

一类区间时变时滞系统的稳定性分析

针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.     

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.     

线性时滞系统稳定性分析综述

时滞在工程领域广泛存在,对此综述了线性时滞系统的稳定性研究方法.从频域和时域两个角度详细介绍了各种方法的特点,着重讨论基于线性矩阵不等式(LMI)的分析方法,指出保守性是分析的重点.对现有结果的保守性进行比较和评述,并提出了改进的思路.     

时滞项可微系统的时滞依赖的稳定性条件

本文研究了带有可微时滞项连续系统的稳定性问题. 通过利用时滞项导数的信息, 给出了改进的时滞系统渐近稳定性条件. 与已有的做法不同, 即便是时滞项导数的上界大于等于 1 时这个上界仍可被利用. 文中证明了所得结果比已有结果的保守性小. 同时, 由于涉及较少的决策变量, 计算复杂度也大为降低. 数例进一步说明了所得结果的有效性和少保守性.     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

离散广义时滞系统的时滞依赖稳定性分析

讨论离散广义时滞系统的稳定性问题. 在不使用系统分解和等价转换的情况下, 利用线性矩阵不等式方法, 给出保证系统正则、因果和稳定的时滞依赖条件. 与已有的方法相比, 本文的方法更加充分地利用时滞的信息, 因此所得结果具有较小的保守性. 数值例子说明本文结果的有效性.     

改进的时变时滞中立型系统的绝对稳定性判据

研究具有时变时滞和扇区有界非线性的中立型系统的绝对稳定性问题.根据时变时滞分段分析思想,构造一个新的Lyapunov-Krasovskii泛函,得到了一些保守性更小的基于线性矩阵不等式的时滞相关绝对稳定性判据.采用凸组合方法,可以避免忽略Lyapunov-Krasovskii泛函微分中的有用项.数值算例表明了所提出方法的有效性.     

Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay

This article considers the problem of delay-dependent stability analysis for a class of discrete-time singular systems with Markovian jump and time-varying delay. The transition probabilities in Markov chain are assumed to be partially unknown. In terms of linear matrix inequality approach, the delay-dependent criteria are proposed to ensure the underlying system to be regular, causal and stochastically stable. Several numerical examples are given to demonstrate the effectiveness and less conservatism of the obtained results.     

Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay

In this paper, we study the issue of finite-time stabilisation for stochastic Markovian jump systems with time-varying delay by considering a new criterion on finite-time stability. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying the finite-time stability of the plant as well as controller synthesis are established in standard linear matrix inequalities. The practical example about a single-link robot arm model demonstrates the validity of the main results.     

Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays

This paper focuses on the problems of globally exponential stability and stabilization with H_∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H_∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.     

Less conservative delay-dependent stability criteria for linear systems with interval time-varying delays

This article provides new delay-dependent stability criteria for linear systems with interval time-varying delays. With a new Lyapunov–Krasovskii functional constructed, a tighter upper bound of its derivative is estimated. The resulting criterion has an advantage over some existing ones in the literature due to the fact that it involves fewer matrix variables and is less conservative, which is established theoretically. Two numerical examples are given to demonstrate the reduced conservatism of the proposed results.     

Stability analysis of Markovian jump systems with delayed impulses

This paper addresses stability for Markovian jump systems with delayed impulses. The delayed impulse has a largely negative effect on the system stability and is not easy to be studied. The main reason is that so many factors such as Markovian switching, impulse, and time-varying delay are simultaneously contained and make its analysis complicated and difficult. In order to analyze these factors clearly, some novel enlarging techniques are presented and used to establish linear matrix inequality (LMI) conditions ultimately. Based on the given methods, more situations such as impulsive instant sequence satisfying a renewal process and Poisson process, respectively, are further studied and better than ones without considering such properties. Two numerical examples are used to show the effectiveness and superiority of the methods.     

广义马尔科夫跳变系统的部分模态依赖观测器设计

针对系统状态变量不完全可测以及系统模态不能实时获得的实际情况,研究广义马尔科夫跳变系统的部分模态依赖观测器及相应控制器的设计问题.基于线性矩阵不等式技术,运用模态依赖的李雅普诺夫函数讨论广义马尔科夫系统的正则和无脉冲特性,给出使系统随机稳定的基于观测器的控制器存在的充分条件.最后通过数值算例验证了所提出设计方法的有效性和优越性.     

Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays

This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.     

Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

This article is devoted to provide further criterion for stochastic stability analysis of semi‐Markovian jump linear systems (S‐MJLSs), in which more generic transition rates (TRs) will be studied. As is known, the time‐varying TR is one of the key issues to be considered in the analysis of S‐MJLS. Therefore, this article is to investigate general cases for the TRs that covered almost all types, especially for the type that the jumping information from one mode to another is fully unknown, which is merely investigated before. By virtue of stochastic functional theory, sufficient conditions are developed to check stochastic stability of the underlying systems via linear matrix inequalities formulation combined with a maximum optimization algorithm. Finally, a numerical example is given to verify the validity and effectiveness of the obtained results.     

Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation

This paper considers the problem of robust H_∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H_∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H_∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.