Simultaneous fault detection and control for switched systems with actuator faults

This paper is concerned with the fault detection and control problem for discrete-time switched systems. The actuator faults, especially ‘outage cases’, are considered. The detector/controller is designed simultaneously such that the closed-loop system switches under an average dwell time, and when a fault is detected, an alarm is generated and then the controller is switched to allow the norm of the states of the subsystem to increase within the acceptable limits. Thus, a switching strategy which combines average dwell time switching with event-driven switching is proposed. Under this switching strategy, the attention is focused on designing the detector/controller such that estimation errors between residual signals and faults are minimised for the fulfillment of fault detection objectives; simultaneously, the closed-loop system becomes asymptotically stable for the fulfillment of control objectives. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. An example comprising of three cases is considered. Through these cases, it is demonstrated that the fault detection and control for switched systems using a two-stage switching strategy and asynchronous switching are feasible.     

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

基于平均驻留时间切换离散线性系统的降阶输出反馈控制

模型降阶作为简化大规模系统的重要工具,一直受到控制界的高度重视.另外,由于在H∞理论指导下所设计的控制器具有维数过高的特点,这将导致控制器的实现和维护受到限制.基于此本文提出了一种平均驻留时间切换离散线性系统降阶输出反馈控制方法.该方法由一个降阶的切换输出反馈控制器和一个对切换控制器在每个切换时刻的状态执行复位规则的监控器组成,该控制器对切换控制器在每个切换时刻的状态进行降阶控制.仿真结果验证了该方法的有效性.     

High-order repetitive control for discrete-time linear switched systems

This paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Simultaneous fault detection and control for switched LPV systems with inexact parameters and its application

This paper investigates the simultaneous fault detection and control problem for a switched linear parameter-varying (LPV) system. The inexact scheduling parameter-dependent fault detection filters and controllers are designed based on the output framework. To realise the detection and control goals, the inexact scheduling parameter-dependent sufficient LMI conditions are obtained by using multiple Lyapunov functions technique. A mode-dependent average dwell-time switching method is used, which is less strict than the general average dwell-time switching method. Simulation results on an aero-engine model show the feasibility and validity of the designed scheme.     

A fault tolerant control framework for periodic switched non-linear systems

An observer-based fault tolerant control (FTC) framework is proposed for a class of periodic switched non-linear systems (PSNS) without full state measurements. Two kinds of faults are considered: continuous faults that affect each mode during its dwell period; and discrete faults that affect the switching sequence. Under the average dwell time scheme, the proposed FTC framework can maintain the stability of overall PSNS in spite of these two kinds of fault. A switched reluctance motor example is taken to illustrate the efficiency of the proposed method.     

Fault detection for continuous‐time switched systems under asynchronous switching

In this paper, the problem of fault detection for continuous‐time switched systems under asynchronous switching is investigated. The designed fault detection filter is assumed to be asynchronous with the original systems. Attention is focused on designing a fault detection filter such that the estimation error between the residual and the fault is minimized in the sense of H _∞ norm. By employing piecewise Lyapunov function and average dwell time techniques, a sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities. Finally, an example of a switched electrical circuit is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Asynchronous fault detection filter design approach for discrete‐time switched linear systems

This paper is concerned with the problem of the fault detection filter design for discrete‐time switched linear systems with average dwell‐time. The designed fault detection filters are also switched systems, which are assumed to be asynchronously switched with the original switched systems. Improved results on the weighted l₂ performance and the H _? performance are first given, and the multiple Lyaounov‐like functions during matched period and unmatched period for the running time of one subsystem are used. By the aid of multiple Lyapunov‐like functions combined with Projection Lemma, the FD filters are designed such that the augmented systems under asynchronous switching are exponentially stable, and the residual signal generated by the filters achieves the weighted l₂‐gain for disturbances and guarantees the H _? performance for faults. Sufficient conditions are formulated by linear matrix inequalities, and the filter gains are characterized in terms of the solution of a convex optimization problem. Finally, examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability of linear discrete switched systems with delays based on average dwell time method

This paper deals with the problem of exponential stability for a class of linear discrete switched systems with constant delays.The switched systems consist of stable and unstable subsystems.Based on the average dwell time method, some switching signals will be found to guarantee exponential stability of these systems.The explicit state decay estimation is also given in the form of the solutions of linear matrix inequalities(LMIs).An example relating to networked control systems(NCSs) illustrates the effect...     

Stability analysis of switched systems under dynamical dwell time control approach

This article investigates the stability of a class of switched systems using dynamical dwell time approach. First, the condition for stability of switched systems whose subsystems are stable are presented with dynamical dwell time approach, which is shown to be less conservative in switching law design than dwell time approach. Then the proposed approach is extended to the switched systems with both stable and unstable subsystems. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.     

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples.     

Stability of switched systems with limiting average dwell time

In this paper, the stability problems of a class of switched systems with limiting average dwell time (ADT) are concerned. The common ADT is improved to a form of limit, and the limiting ADT even can be infinite. Different from previous results, in order to take full advantage of stabilizing switchings, switching‐dependent switched parameters are first used to describe the relationship of two consecutive activated switchings. Then, stability criteria of switched systems with limiting ADT are established, which are less conservative comparing with the existing results. Additionally, some stability criteria of switched systems including continuous‐time and discrete‐time cases are derived. Finally, the validity and effectiveness of our results are elucidated by numerical examples.     

Asynchronously switched control of switched linear systems with average dwell time

This paper concerns the asynchronously switched control problem for a class of switched linear systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. The so-called asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By further allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are first derived. Then, the asynchronously switched stabilizing control problem for linear cases is solved. Given the increase scale and the decrease scale of the Lyapunov-like function and the maximal delay of asynchronous switching, the minimal ADT for admissible switching signals and the corresponding controller gains are obtained. A numerical example is given to show the validity and potential of the developed results.     

Stability analysis for networked control systems based on average dwell time method

This paper studies the problem of the exponential stability of networked control systems (NCSs) with large delay periods, which often appear in the transmission of NCSs. Some new concepts about large delay periods are introduced, and a method based on switching is employed. The maximum allowable transfer interval is obtained such that the considered system is exponentially stable. The criteria obtained contain existing results without considering a large delay period as a special case. An example is given to show the effectiveness of the proposed criteria. Copyright © 2009 John Wiley & Sons, Ltd.     

Output regulation of switched linear multi-agent systems: an agent-dependent average dwell time method

The output regulation problem of switched linear multi-agent systems with stabilisable and unstabilisable subsystems is investigated in this paper. A sufficient condition for the solvability of the problem is given. Owing to the characteristics of switched multi-agent systems, even if each agent has its own dwell time, the multi-agent systems, if viewed as an overall switched system, may not have a dwell time. To overcome this difficulty, we present a new approach, called an agent-dependent average dwell time method. Due to the limited information exchange between agents, a distributed dynamic observer network for agents is provided. Further, a distributed dynamic controller based on observer is designed. Finally, simulation results show the effectiveness of the proposed solutions.     

Unified mode‐dependent average dwell time stability criteria for discrete‐time switched systems

In this article, a unified mode‐dependent average dwell time (MDADT) stability result is investigated, which could be applied to switched systems with an arbitrary combination of stable and unstable subsystems. Combined with MDADT analysis method, we classified subsystems into two categories: switching stable subsystems and switching unstable subsystems. State divergence caused by switching unstable subsystems could be compensated by activating switching stable subsystems for a sufficiently long time. Based on the above considerations, a new globally exponentially stability condition was proposed for discrete‐time switched linear systems. Under the premise of not resolving the LMIs, the MDADT boundary of the new stability condition is allowed to be readjusted according to the actual switching signal. Furthermore, the new stability result is a generalization of the previous one, which is more suitable for the case of more unstable subsystems. Some simulation results are given to show the advantages of the theoretic results obtained.     

任意相对阶下非线性切换系统的事件触发漏斗控制

针对一类具有任意相对阶且带有部分非输入到状态稳定逆动态的非线性切换系统, 提出一种动态事件触 发漏斗跟踪控制方案. 首先, 引入一个虚拟输出将任意相对阶的非线性切换系统转换为相对阶为一的非线性切换系 统. 其次, 设计各子系统的事件触发漏斗控制器和切换的动态事件触发机制, 解决候选事件触发漏斗控制器和子系 统之间的异步切换问题, 所提方案消除已有文献中为所有子系统设计共同控制器带来的保守性. 在一类具有平均驻 留时间切换信号的作用下, 保证切换闭环系统的所有信号都是有界的, 且跟踪误差一直在预设的漏斗内演化, 并排 除采样中的奇诺现象. 最后, 一个仿真例子验证方案的实用性和有效性.     

Robust stability and controller synthesis of discrete linear switched systems with dwell time

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l ₂-gain analysis where a bounded real lemma is derived, and to H _∞ control and estimation, both for the nominal and the uncertain cases.     

Event-triggered average dwell time control for switched uncertain linear systems with actuator saturation

This paper investigates an event-triggered average dwell time (ADT) control method for switched systems with dynamic uncertainty and actuator saturation. An event-trigger is employed and only few necessary data are authorised to be transmitted to the controller by the event-trigger when its threshold is violated. Since the time-intervals of system switching signal and data releasing time-intervals of the event-trigger share common time-sequence yet not inter-influenced, an ADT control law is proposed for guaranteeing system exponential stability; meanwhile, the actuator saturation limitation is also considered. More significantly, a minimal data releasing time-interval of the event-trigger is given and it has been proved that the event-trigger cannot be violated during that time-interval. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Fault detection for switched nonlinear systems under asynchronous switching

Asynchronous switching between switched system and associated filter or controller frequently occurs in several applications. In this article, the fault detection problem for a class of switched nonlinear systems with asynchronous switching is addressed. To model the switched system behaviour under asynchronous switching, two working modes are adopted to facilitate the studies on the issue. Then, based on average dwell time approach, a fault detection filter is developed via solving LMIs. Furthermore, it is proved that the fault detection problem under synchronous switching is only a particular case of our results for asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of proposed results.