Stabilisation for switched linear systems with time-varying delay and input saturation

This article investigates the stabilisation problems for continuous-time and discrete-time switched systems with time-varying delay and saturated control input. Based on dwell time switching signals and multiple Lyapunov functional method, stabilisation conditions are well obtained in the context of linear matrix inequalities. To estimate attractive regions as large as possible, the feasibility problems are translated into optimisation problems. In addition, the corresponding results are presented for linear time-delay systems and switched delay-free systems, which improve and supplement some existing ones in the literature. Finally, numerical examples and simulations are given to illustrate the effectiveness and values of the proposed results.     

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H_? and H_∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.     

区间化时变时延的网络化切换系统建模与控制

研究了具有从传感器到控制器和控制器到执行器存在双边时变时延的网络控制系统指数稳定性的问题.首先将时延变化范围划分为多个等分区间,然后采用增广矩阵的方法建立了参数不确定的离散时间切换闭环系统模型.同时基于平均驻留时间分析方法,给出了系统满足指数稳定的条件,接着进一步的建立了时延区间划分个数与系统状态指数衰减率的定量关系.该方法有效降低了系统设计的保守性,一定程度上减少了系统状态收敛的时间.最后通过数值仿真验证了所提方法的有效性.     

一类带有变时滞的广义切换系统的滑模控制

研究一类具有非匹配不确定性和变时滞的广义切换系统的滑模控制问题.首先,基于Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,针对每个子系统设计对应的积分型滑模面,给出了每个滑动模态方程鲁棒渐近稳定的充分条件;然后,设计了滑模控制器及切换规则,使得闭环系统的状态能够到达滑模面上,产生滑动模态;最后以仿真实例说明了所提出方法的有效性.     

Interval estimator design for switched systems with its application

This paper is concerned with the interval estimation issue for switched systems subject to the bounded noise signal and disturbance signal. By virtue of the positiveness feature of the interval estimation error dynamics, the multiple co-positive Lyapunov functions strategy is presented to build the interval estimators for the switched linear systems under the dwell-time dependent switching signal. A new criterion is driven to ensure the boundedness of the interval estimation errors. This criterion can be checked by linear programming technique. In the end, a beneficial application of estimating the speeds of an engine model is offered to verify the estimation performances of the established interval estimation technique.     

Input-to-state stability for discrete-time time-varying impulsive switched delayed systems with asynchronous phenomena

This paper studies the input-to-state stability (ISS) for a class of discrete-time time-varying impulsive switched delayed systems, in which the asynchronous phenomena are considered. Asynchronous phenomena here include two implications: asynchronous impulses and switches and asynchronous switching. The former means that the events, that is, impulses and switches, are not necessary to occur simultaneously, while the latter indicates that the actual switching modes and related controllers or specified modes do not coincide. Applying the mode-dependent concept to impulses and switches, both the improved Krasovskii-type and Razumikhin-type ISS criteria are provided. The time differences of Lyapunov functionals or functions here are sign-changing and time-varying, releasing from the traditional assumption that always requires negative definiteness. Meanwhile, in this paper, ISS or non-ISS subsystems and stabilizing or destabilizing impulses are taken into account. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.     

一类时滞切换系统的稳定性分析

利用时滞分解和平均驻留时间方法讨论一类时滞切换系统的稳定性问题.定义了更为一般的Lyapunov函数,结合Jensen积分不等式和倒数凸组合技术得到的线性矩阵不等式条件具有更小的保守性和更低的计算复杂性给出的仿真算例进一步验证了所得结果的有效性.     

Fault recoverability analysis of switched systems

This article provides an approach to evaluate the fault recoverability of switched systems (SS) under given energetic constraints. Such evaluation reveals the capability of the SS to tolerate the worst faults over a prescribed set under possible energy constraints. The evaluation is achieved by using the smallest eigenvalue of a proposed ‘switched-system controllability Gramian’. Simulation results about a longitudinal flight control process example are presented to show the effectiveness of the proposed method.     

一类MIMO非线性时滞系统的鲁棒自适应控制

针对一类具有非线性输入的MIMO时变时滞系统,基于变结构控制原理,提出了一种稳定自适应控制器设计的新方案.该方案通过使用Lyapunov-Krasovskii(L-K)泛函抵消了因未知时变时滞带来的系统不确定性;进一步,利用Young's不等式和参数自适应估计取消了非线性死区输入模犁和不确定项假设中各种参数均为已知的要求.通过理论分析,证明了闭环控制系统半全局一致终结有界,跟踪误差收敛到零的一个邻域内.     

一类时滞切换系统的输入-状态稳定性分析

利用多Lyapunov函数方法、驻留时间法和Gronwall-Bellman不等式研究了一类时滞切换系统的输入-状态稳定性分析问题．从系统输入-状态稳定定义出发,给出了使得一类时滞切换系统输入-状态稳定的充分条件．与已有的方法相比,无需同时满足构造输入-状态稳定控制Lyapunov函数和所有子系统都是输入-状态稳定的条件,为控制器的设计提供了便利．最后,通过算例仿真验证了所提出方法的可行性．     

Razumikhin stability theorems for a general class of stochastic impulsive switched time‐delay systems

This paper studies stability of a general class of impulsive switched systems under time delays and random disturbances using multiple Lyapunov functions and fixed dwell‐time. In the studied system model, the impulses and switches are allowed to occur asynchronously. As a result, the switching may occur in the impulsive intervals and the impulses can occur in the switching intervals, which have great effects on system stability. Since the switches do not bring about the change of the system state, we study two cases in terms of the impulses, ie, the stable continuous dynamics case and the stable impulsive dynamics case. According to multiple Lyapunov‐Razumikhin functions and the fixed dwell‐time, Razumikhin‐type stability conditions are established. Finally, the obtained results are illustrated via a numerical example from the synchronization problem of chaotic systems.     

Event-triggered control for switched delay systems with dynamic input quantization

This paper is concerned with event-triggered control for the switched system with time-varying delay and dynamic input quantization. The work is aimed at solving the quantizer saturation in the finite-level quantized control design and the mismatch caused by event-triggered sampling and the switching. First of all, the quantization parameter updating laws are designed respectively in the case of match and mismatch between the system and the controller under the event-triggered mechanism without Zeno behavior. Then, the total variation of Lyapunov functional is transformed into discrete time updating of the dynamic quantization parameter. A switching law and a quantized control strategy are developed to ensure the exponential stability of switched systems with delay and input quantization. At last, two examples are given to illustrate the validity of the results.     

Output tracking control of switched nonlinear systems with multiple time-varying delays

In this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.     

Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH_∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.     

Fault accommodation for linear systems with time-varying delay

This paper studies the fault accommodation problem for linear systems with time-varying delay, system uncertainties and external disturbances. A novel intermediate estimator-based fault tolerant control (FTC) scheme is proposed, where an intermediate estimator is constructed to estimate the states and the faults simultaneously, based on the estimation; an FTC compensation scheme is designed to eliminate the effects of faults, system uncertainties and time-varying delay. It is proved that the states of the closed-loop system are uniformly ultimately bounded. A simulation example shows the effectiveness of the proposed method.     

Robust reliable control of switched uncertain systems with time-varying delay

This paper is concerned with reliable control problems for the switched uncertain systems with time varying delay. A method for designing robust reliable controller is presented by means of the multiple Lyapunov functions technique so that the energy-like functional does not have to decrease along the switching instants. The proposed controller is reliable in that it can guarantee the closed loop asymptotic stablility of switched delay systems in the case of the possible presence of failures of partial actuators. Delay independent results of the reliable controller design are presented in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the applicability of the proposed results.     

不确定时变时滞切换广义系统的鲁棒H∞ 保性能控制

利用公共 Lyapunov 泛函方法和凸组合技术研究了一类不确定时变时滞切换广义系统的鲁棒 ∞保性能控制和状态反馈镇定问题.在设定的切换规则下,给出了基于线性矩阵不等式表示的鲁棒 ∞保性能控制器存在的充分条件,保证了系统具有鲁棒 ∞干扰抑制水平 及状态反馈可切换镇定的同时满足保性能指标.最后的仿真示例验证了该方法的有效性.     

Switching strategy in tracking constant references for linear time-varying delay systems with actuator failures

Tracking of command constant references is a tracking control problem of fundamental importance. This problem for linear time-varying delay systems in the presence of actuator failures is solved in this article. The linear time-varying delay system with actuator failures is modelled as a switched linear time-varying delay system by utilising switching systems theory and a suitable control scheme. The polytopic technique is employed in order to cope with the time-varying, delay-derivative term in case its absolute value might exceed one. On the grounds of the average dwell-time approach, a switching tracking control law that is immune to actuator failures is designed and the conditions are derived such that the output of the linear time-varying delay system tracks given constant command references. Two illustrative examples along with the respective numerical and simulation results are presented to demonstrate the effectiveness of the proposed method.     

一类具有变时滞不确定分布参数系统的滑动模控制

研究一类不确定变时滞分布参数系统的滑动模控制问题．首先设计一种无记忆功能的变结构控制器;然后分析了在滑动模切换面上滑动模控制系统关于不确定量的不变性特征;最后给出了从任意初始位置出发的轨线到达滑动模态区的时间估计．研究表明,所设计的控制器结构简单．容易实现．     

含有未知控制方向的非线性时滞系统学习控制

本文对于一类含有未知控制方向及时滞的非线性参数化系统,设计了自适应迭代学习控制算法.在设计控制算法过程中采用了参数分离技术和信号置换思想来处理系统中出现的时滞项,Nussbaum增益技术解决未知控制方向等问题.为了对系统中出现的未知时变参数和时不变参数进行估计,分别设计了差分及微分参数学习律.然后通过构造的Lyapunov-Krasovskii复合能量函数给出了系统跟踪误差渐近收敛及闭环系统中所有信号有界的条件.最后通过一个仿真例子说明了控制器设计的有效性.