On passivity of state delayed stochastic jump systems

1.INTRODUCTION Stochasticjumpsystemisaspecialkindofhybridsys tems.Itisdescribedbyacontinuous timefinite state Markovprocesswhichreferstothemode,andbya dynamicsystemofdifferentialequationswhichrefers tothestate.Thejumpsystemscanmodelthedynam icsystemssubjecttoabruptvariationintheirstruc turesandthereforattractresearchinterestinginthe world.Recently,thereweresomeresearchesoncon trolproblemsforjumpsystemswithtimedelay[1,2].Passivityplaysanimportantroleinsystemand controltheory.Butalmostallr…     

Delay-dependent passive control of linear systems with nonlinear perturbation

The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive. In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity. Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities （LMIs）. In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.     

基于时滞分割法的Markov随机切换系统指数稳定性

研究了时变时滞满足h₁≤d(t)≤h₂的Itô型随机Markov切换系统的区间时滞相关指数稳定性。基于时滞分割的思想,建立了新颖的Lyapunov-Krasovskii泛函,并引入一些改进的积分等式,以线性矩阵不等式的形式给出了低保守性的区间时滞相关指数稳定条件。最后用几个数值算例说明该结论的有效性及其较低的保守性。     

Delay-dependent robust passivity control for uncertain time-delay systems

The robust passivity control problem is addressed for a class of uncertain delayed systems with time-varying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality(BMI),which ensures a prescribed stochastic robust H∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed. The parameter uncertaintie is assumed to be time varying norm-bounded. First, the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method. Then, a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality (BMI), which ensures a prescribed stochastic robust H∞ performance level for the resulting closed loop system with nonzero disturbance input and for all admissible uncertainties. An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: a delay decomposition approach

The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters.By decomposing the delay interval into multiple equidistant subintervals,a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique.Besides,the decay rate has no conventional constraint and can be selected according to different practical conditions.Finally,two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

随机时延网络控制系统的鲁棒H∞状态反馈控制

研究了含有双随机时延的不确定网络控制系统的鲁棒H_∞状态反馈控制问题。将传感器到控制器和控制器到执行器的网络时延建模为相互独立的连续时间离散状态的马尔可夫随机过程。基于此网络环境,构造时延依赖的控制器,将不确定网络控制系统转化为马尔可夫跳变系统。通过Lyapunov Krasovskii泛函方法和新的矩阵不等式技术,给出了系统随机稳定且满足H_∞性能的充分条件,并以矩阵不等式形式给出了相应的控制器设计方法。最后,给出了仿真算例,验证了该方法的有效性。     

Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It Stochastic Systems

1. INTRODUCTIONIn this paper, we investigate the decentralized stabilization of the large-scale delay It6 stochastic system, aswhere fi E Rut is state vector of the ith subsystem, m e Rmi is input vector of the ith subsystem: Al(t), Fi.(t) E R"' xni I Bi(t) E Rut xos are bounded and piecewise continuous matrixm mhmctions, aAi E R"i"', FBi e R"'"m', ac = al ZNi = N; r(.) E RP, P(.) E Rqj~1 i=1are Lebesgue measurable; W(t) ~ (Wll(t),'' I WIN, (t),'' Wml(t),..., WANd (t))" …     

Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay Ito Stochastic Systems

In this paper, we investigate the decentralized stabilization of some time-varying uncer tain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.     

基于观测器的时滞依赖鲁棒无源控制

研究一类带有参数不确定性和时变时滞的不确定线性系统的鲁棒无源控制问题。针对标称系统,利用线性矩阵不等式给出其时滞依赖无源性条件;讨论当系统的系数矩阵出现参数不确定时,存在基于观测器的控制器使得闭环系统是强鲁棒稳定且严格无源的时滞依赖性充分条件。构造出期望的观测器和控制器。数值算例说明结论的有效性。     

Robust H∞ control for uncertain stochastic saturating systems with time delays

The robust H∞ control problem for uncertain stochastic time-delay systems containing nonlinear actuators is considered. The uncertainties in the systems are assumed to satisfy specific match condition. The time delays exitst in state as well as control input. The new stochastic robust stabilization criterion and a sufficient condition for the existence of stochastic robust stabilizing control law are derived. The delay-independent memoryless robust H∞ controllers are constructed to stabilize the given systems in terms of a group of linear matrix inequalities. A numerical simulation example is presented to show that the proposed approach is valid.     

含时变时滞函数的GM(1,1|τ_i)模型及其应用

针对带有时滞效应的小样本数据序列的预测建模问题,现有模型通常假设时滞期为固定值,忽略了时滞值动态变化对模型效果的影响.为了克服这一局限性,本文考虑系统时滞的动态变化效应,将GM(1,1|τ,r)模型的静态时滞参数推广为时变时滞函数,设计出非整数时滞取值区间对应的时变时滞参数表达式.提出以灰关联理论为基础的时变时滞函数的参数优化方法,推导出GM(1,1|τ_i)模型参数估计值以及预测序列的时间响应式.该方法不仅提高了模型对所分析序列的拟合度,还可充分利用时滞参数函数的数学性质,进一步研究时滞因素对系统发展趋势的影响.最后,将GM(1,1|τ_i)模型应用于福建省全省沿海港口货物吞吐量预测,并将建模预测结果与经典的GM(1,1)模型和GM(1,1,τ)模型进行比较.结果表明当原始序列具有时滞效应时,GM(1,1|τ_i)模型具有更高的建模精度,能够反映出更为复杂的系统时滞变化情况,扩展了含时滞参数灰色预测模型的适用范围.     

Guaranteed cost control for discrete-time networked control systems with random Markov delays

The guaranteed cost control for a class of uncertain discrete-time networked control systems with random delays is addressed.The sensor-to-controller (S-C) and contraller-to-actuator (C-A) random network-induced delays are modeled as two Markov chains.The focus is on the design of a two-mode-dependent guaranteed cost controller,which depends on both the current S-C delay and the most recently available C-A delay.The resulting closed-loop systems are special jump linear systems.Sufficient conditions for existence of guaranteed cost controller and an upper bound of cost function are established based on stochastic Lyapunov-Krasovakii functions and linear matrix inequality (LMI) approach.A simulation example illustrates the effectiveness of the proposed method.     

T-S模糊时滞系统的鲁棒无源控制

基于Lyapunov稳定性理论,时具有参数不确定性的T-S模糊时滞系统的鲁棒稳定性和无源性进行了研究.具有参数不确定性的T-S模糊模型可以任意精度近似连续非线性不确定系统.假设系统中的参数不确定性是范数有界的.运用Lyapunov稳定性理论给出了鲁棒无源控制器存在的充分条件.通过解一组线性矩阵不等式(LMIs),可直接获得鲁棒无源控制器.所设计的鲁棒无源控制器能够保证对于T-S模糊时滞系统中所有的参数不确定性,闭环系统都是鲁棒稳定的并且是严格无源的.并且,通过求解带有约束条件的线性矩阵不等式问题,可以设计出具有最大耗散率的鲁棒无源控制器.数值例子验证了所提出设计方法的有效性.     

考虑时延与丢包的网络控制系统分析与综合

针对具有时变网络诱导时延和丢包问题的网络控制系统稳定性分析与控制器设计问题,通过考虑网络诱导时延是时变和有界的情形,并分析网络诱导时延与其上界之间的关系,应用Lyapunov-Krasovskii泛函结合积分不等式方法,提出了一种改进的、同时考虑了网络诱导时延和丢包问题的网络控制系统稳定条件,并基于改进的锥补线性化迭代算法（improved cone complementary linearization, ICCL）给出了一种具有更低保守性的控制器设计方法。数值实例表明上述方法的有效性。     

Ho∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system (NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller (S/C) and from controller to actuator (C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

New type of adaptive control for a class of distributed time-delay systems with adaptation regard to delay parameter

The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is proposed for a memory proportional and integral (PI) feedback controller with adaptation to distributed time-delay. The feedback controller with memory simultaneously contains the current state and the past distributed information of the addressed systems. The design for adaptation law to distributed delay is very concise. The controller can be derived by solving a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the design method.     

一类T-S 模糊广义系统的无源控制

研究了一类T-S模糊广义系统的无源控制问题.通过矩阵分解方法,证明了这类系统容许的充分必要条件.在此基础上,将严格无源的概念引入到T-S模糊广义系统中,得到了使闭环系统容许、严格无源的充分条件,并将此条件用线性矩阵不等式(LMIs)表示.通过解这些矩阵不等式得到状态反馈增益矩阵.这个充分条件,可以一次判定系统的容许、严格无源.最后的数值算例说明所给方法的可行、有效.