Stabilisation of a class of positive switched nonlinear systems under asynchronous switching

This paper addresses the stabilisation problem for a class of positive switched nonlinear systems under asynchronous switching, which means that the switches between the candidate controllers and the system modes are not synchronous. The continuous and discrete cases are considered respectively. Sufficient conditions are firstly provided for the existence of the asynchronous switching controllers to guarantee the closed-loop system to be positive and exponentially stable, and the corresponding admissible switching signals are presented. As a special case, the stabilisation results for positive switched linear systems under asynchronous switching are provided accordingly. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Input‐to‐state stability of impulsive switched nonlinear time‐delay systems with two asynchronous switching phenomena

This summary addresses the input‐to‐state stability (ISS) and integral ISS (iISS) problems of impulsive switched nonlinear time‐delay systems (ISNTDSs) under two asynchronous switching effects. In our investigated systems, impulsive instants and switching instants do not necessarily coincide with each other. Meanwhile, systems switching signals are not simultaneous with the corresponding controllers switching signals, which will induce instability seriously, and cause many difficulties and challenges. By utilizing methods of Lyapunov‐Krasovskii and Lyapunov‐Razumikhin, mode‐dependent average dwell time approach, and mode‐dependent average impulsive interval technique, some stability criteria are presented for ISNTDSs under two asynchronous switching effects. Our proposed results improve the related existing results on the same topic by removing some restrictive conditions and cover some existing results as special cases. Finally, some simulation examples are presented to illustrate the effectiveness and advantages of our results.     

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.     

Stabilization of positive switched systems with time-varying delays under asynchronous switching

This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods.     

异步时滞切换正系统的有限时间镇定

研究异步切换下时滞切换正系统的有限时间控制问题,即针对控制器切换滞后于子系统切换形成的异步现象,基于平均驻留时间切换方法对切换正系统开展有限时间镇定研究.首先,将每个正子系统运行的区间划分为子系统与控制器匹配和失配区间,并构造多余正Lyapunov-Krasovskii泛函;其次,基于有限时间稳定理论,实现平均驻留时间切换律及异步时滞切换正系统有限时间镇定控制器的联合设计,并给出连续时间和离散时间两种情形下系统有限时间镇定的充分条件;最后,通过两个仿真例子验证所提出方法的有效性.     

基于模型依赖驻留时间的异步切换控制

研究在模型依赖平均驻留时间切换策略下切换线性系统的异步切换控制问题,同时考虑模型依赖的控制器滞后时间的约束问题.在实际情况下,信号传输和系统检测等原因会导致控制器的切换滞后于子系统.基于这类情况,首先将子系统运行的区间划分为子系统与控制器相匹配的区间和非匹配的区间,根据模型依赖的驻留时间策略设计出各子系统的控制器;然后,结合模型依赖的控制器滞后时间、系统参数和Lyapunov稳定条件推导出合适的驻留时间设计参数,且使得异步切换系统全局一致指数稳定;最后通过数值仿真验证了所提出方法的有效性.     

Stability Properties of Switched Nonlinear Delay Systems with Synchronous or Asynchronous Switching

This paper is concerned with the problem of input‐to‐state stability (ISS) for a class of switched nonlinear delay systems. The cases where the switching signal of the system and the switching signal of the corresponding controller are synchronous and asynchronous are both considered. To study two asynchronous switching signals in a unified framework, we adopt the technique of the merging switching signal. Based on a piecewise Lyapunov–Krasovskii functional method, some sufficient conditions are explicitly given to guarantee the ISS of the switched nonlinear delay system under the average dwell time scheme. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory.     

Stability and stabilization of switched stochastic systems under asynchronous switching

This paper studies the stability and stabilization problems for a class of switched stochastic systems under asynchronous switching. The asynchronous switching refers to that the switching of the candidate controllers does not coincide with the switching of system modes. Two situations are considered: (1) time-delayed switching situation, that is, the switching of the candidate controllers has a lag to the switching of the system modes; (2) mismatched switching situation, the switching of the candidate controllers does not match the switching of the system modes. Using average dwell time and Lyapunov-like function, sufficient conditions are established for stochastic input-to-state stability of the whole system. Also, the stabilizing controller design approach is proposed for switched stochastic linear systems. The minimal average dwell time and the controller gain are achieved. Finally, a numerical example is used to demonstrate the validity of the developed results.     

Sojourn-probability-dependent H∞ control for networked switched systems under asynchronous switching

This paper considers H_∞ controller design for a class of networked switched discrete systems under asynchronous switching. The sojourn probability information – the probability of the switched systems staying in each subsystem – is first used to rebuild the networked switched systems. Also, a time-varying lag, depending on both the network-induced delays and switching signals, is taken into consideration between the switching instants of the controllers and systems model. By considering both sojourn probability information and asynchronous switching, a new kind of networked switched system model is proposed, wherein a set of random variables are proposed to describe the sojourn probabilities of the subsystems. Then, stability analysis and H_∞ performance analysis under asynchronous switching are derived. It should be noted that the system performance depends not only on the time-varying lag, but also on the sojourn probabilities. Finally, an example is given to illustrate the effectiveness of the proposed approach.     

Stability,L2‐gain and asynchronous H ∞ control for continuous‐time switched systems

This paper is concerned with the stability and L₂‐gain problems for a class of continuous‐time linear switched systems with the existed asynchronous behaviors, where ‘asynchronous’ means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L₂‐gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H _∞ control. Based on the result, the mode‐dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive tracking control for uncertain switched systems under asynchronous switching

This paper addresses the state‐tracking model reference adaptive control problem for a class of switched systems with parametric uncertainties, where switchings between subsystems and designed adaptive controller are asynchronous. First, we establish a stability criterion for a switched reference model and convert the state‐tracking problem into the stability problem of an error switched system. Then, an adaptive law is designed, and the global practical stability of the error switched system is guaranteed under a class of switching signals characterized by a dwell‐time condition. An electrohydraulic system is given as an example to demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust resilient control for impulsive switched systems under asynchronous switching

The robust resilient control problem is addressed for a class of impulsive switched systems under asynchronous switching. Through constructing the piecewise Lyapunov function, a robust resilient controller is designed initially, which, for all admissible uncertainties, guarantees that the corresponding closed-loop system is exponentially stable under asynchronous switching signals. Here, the average dwell time method is utilized and the estimate of the trajectory is also presented. For the convenience of computation, all conditions are cast into the form of linear matrix inequalities. Finally, numerical examples and simulation results are demonstrated to illustrate the correctness and effectiveness of the proposed approach.     

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.     

Control discrete-time switched singular systems with state delays under asynchronous switching

This article is concerned with the problem of state feedback control for a class of discrete-time switched singular systems with time-varying state delays under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the system modes. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence a stabilising switching law is first derived to guarantee the regularity, causality and exponential stability of the closed-loop system in the presence of asynchronous switching. The stabilising switching law is characterised by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

H ∞ output-feedback control for switched linear discrete-time systems with time-varying delays

In this paper, the problem of H _∞ output feedback control for switched linear discrete-time systems with time delays is investigated. The time delay is assumed to be time-varying and bounded. By constructing a switched quadratic Lyapunov function for the underlying system, both static and dynamic H _∞ output feedback controllers are designed respectively such that the corresponding closed-loop system under arbitrary switching signals is asymptotically stable and a prescribed H _∞ noise-attenuation level bound is guaranteed. A cone complementary linearization algorithm is exploited to design the controllers. A numerical example is presented to show the effectiveness of the developed theoretical results.     

Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time

This paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.     

一类含有输入时滞的不确定切换系统的鲁棒指数镇定

针对一类含有输入时滞的不确定切换系统,讨论了鲁棒指数镇定问题,提出了可行的切换控制器和切换信号的设计方法．首先,运用还原法将具有时滞的切换系统转化为无时滞的切换系统;然后,基于线性矩阵不等式,给出了系统在切换控制器和切换信号作用下鲁棒指数可镇定的充分条件,并利用多Ｌｙａｐｕｎｏｖ函数方法给出了定理的详细证明;最后,利用数值仿真例子验证了该方法的有效性．     

Exponential Stability and Asynchronous Stabilization of Switched Systems With Stable and Unstable Subsystems

This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.     

On modeling and secure control of cyber‐physical systems with attacks/faults changing system dynamics: An average dwell‐time approach

The problem of secure control in cyber‐physical systems is considered in this work. A new modeling framework is first introduced, ie, cyber‐physical systems with attacks/faults changing system dynamics is modeled as a switched system, where the switching among subsystems is triggered by a rule generated by attackers but unknown for defenders. Based on an average dwell‐time approach incorporated by the attack frequency and duration properties, a convergence condition of the Lyapunov function on active intervals of subsystems (ie, the attack and healthy modes), under the developed switched controller, is given. Next, the unknown rule, however, leads to the asynchronous switching problem between the candidate controllers and system modes. As a result, degradation of the system performance (eg, a large chatter occurred in the system state trajectories) in the asynchronous intervals is caused. To address the difficulty, a novel switching law based on a prescribed performance is proposed, and it is shown that the asynchronous intervals are shortened by reducing adjustable parameters in the switching law. An illustrative example verifies the effectiveness of the proposed method.     

Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.