一类具有输入时滞的切换系统的正性镇定

研究一类含有输入时滞的切换系统正性镇定问题.通过引入增广系统,将时滞作为一个切换参数,原系统的正性镇定问题转化为增广系统异步切换下的控制问题.利用对偶系统的特性,得到增广系统在平均驻留时间切换下为正且稳定的充分条件,进而设计控制器以保证闭环系统的正性和稳定性.得到的充分条件可转化为标准的线性规划问题,利用Matlab的linprog工具箱进行求解.最后,通过仿真示例验证了所得结果的有效性.     

切换非线性正系统的有限时间稳定性

研究模型依赖平均驻留时间(MDADT)切换信号下一类齐次度为1的切换非线性正系统的有限时间稳定问题.首先,通过构造恰当的切换最大分离Lyapunov函数,借助于Dini导数,基于MDADT切换信号,给出切换非线性正系统有限时间稳定的充分条件.与已有的指数稳定性结果相比,进一步说明有限时间稳定与指数稳定的区别.其次,将所得结论应用于切换线性正系统,得到切换线性正系统在MDADT或平均驻留时间(ADT)切换信号下有限时间稳定的充分条件.最后,通过仿真算例验证所得结论的有效性.     

带有混合时滞的切换系统的耗散性分析与控制

本文研究了一类具有不稳定子系统和混合时滞的切换系统的耗散性和指数镇定问题. 首先, 为了消除不稳 定子系统给这类时滞系统带来的不利影响, 采用了一种新颖的切换信号设计方法–将模态依赖平均驻留时间的慢切 换和快切换方法相结合, 并通过利用Lyapunov相关理论, 给出了全局指数稳定的充分条件. 然后, 利用耗散性理 论、多重Lyapunov-Krasovskii泛函技术、积分不等式、与Schur补引理等方法, 以线性矩阵不等式的形式给出了耗散 性能的相关判据, 使闭环系统实现全局指数稳定性的同时具有严格耗散性能. 进一步, 在给定扰动衰减水平的前提 下, 通过求解一些严格的LMI条件, 建立了一组可行控制器. 最后, 通过仿真实例验证了该方法的有效性.     

时滞执行器饱和Markov跳变系统的有限时间镇定

讨论了含执行器饱和的离散时滞Markov跳变系统在未知但有界扰动的情况下,针对系统模态转移概率部分未知的系统进行有限时间镇定的分析和研究。利用构造的Lyapunov函数和饱和非线性处理技术,对具有执行器饱和的离散时滞Markov系统进行研究,并提出了系统状态有限时间镇定的充分条件,结合线性矩阵不等式的方法,设计并实现了有限时间镇定状态反馈控制器。通过数值仿真,示例验证了该设计方法的有效性及潜在的应用性。     

基于驻留时间切换下离散切换系统的异步控制器设计

针对一类切换线性系统,本文提出了一种基于系统状态的驻留时间策略.这种切换策略不仅使异步状态反馈切换系统稳定,而且缩短了系统的运行时间.对于异步切换系统的稳定性和增益问题,本文主要的结论是在子系统运行期间Lyapunov函数允许增加,同时又没有的限制.通过利用基于系统状态的驻留时间策略,推导出了切换线性系统的控制器设计的充分条件.得出的结论也可以推广到非线性切换系统.本文中最后给出的算例用于说明该方法的有效性.     

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...     

倾转旋翼机过渡飞行模式的有限时间切换控制

基于有限时间切换控制方法,研究倾转旋翼机过渡模式,即短舱倾角从$0^{\circ     

离散区间线性切换正系统的镇定

这里同时考虑了快切换和慢切换两类切换情形, 即任意切换和平均驻留时间切换情形. 在这两种情形下, 均给出了系统状态反馈镇定控制器的存在条件, 所设计的控制器能够在原系统不必为正的情况下保证相应的闭环系统对于所有给定的区间不确定性不但为正而且渐近稳定. 由于所获得的控制器存在条件均被描述为了线性不等式的形式, 因此通过求解简单的线性规划问题很容易确定出所期望的控制器参数. 最后, 通过数值算例说明了本文所提出的镇定控制器设计方法的有效性.     

具有输入时滞的随机前馈非线性系统的状态反馈镇定

针对一类具有输入时滞的随机前馈非线性系统, 首次研究了它的状态反馈镇定问题. 首先引入一个变量变换, 将其与齐次占优方法巧妙结合, 通过构造合适的 Lyapunov-Krasovskii 泛函, 设计了一个状态反馈控制器, 使得闭环系统的平衡点依概率全局渐近稳定.     

离散切换线性系统的异步滤波器设计

利用模型依赖的平均驻留时间策略研究离散异步切换线性系统的指数H_∞滤波问题.考虑到在实际问题中,所设计的模型依赖的全阶滤波器的切换往往会滞后于其相应的子系统,将子系统的运行区间划分为与滤波器匹配的区间和不匹配的区间.针对两种工作模态,利用模型依赖的平均驻留时间切换策略和μ依赖的多Lyapunov函数方法完成滤波器的设计,并使得增广得到的异步滤波误差系统全局一致指数稳定且满足指数H_∞性能指标.该滤波器存在的充分条件在文中以线性矩阵不等式的形式给出.最后通过数值仿真验证所提方法的有效性.     

Positive stabilization for switched linear systems under asynchronous switching

This paper is concerned with the positive stabilization for a class of switched systems under asynchronous switching signals. Because it inevitably takes some time to identify the active subsystem in the real systems and activate the corresponding controller, the switching of controllers lags behind that of subsystems, which arises the problem of the asynchronous switching. By analyzing the solution of dynamic systems, the mode‐dependent controllers are designed to guarantee the positivity and exponential stability for the resultant closed‐loop switched linear systems under asynchronous switching signals in continuous‐time and discrete‐time cases, respectively. Sufficient conditions for the existence of admissible state‐feedback controllers are developed, and the corresponding switching signals are designed. Furthermore, a synchronous switching phenomenon is discussed as a special case. Finally, numerical examples are given to illustrate the effectiveness of the results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

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.     

Finite-time stability and stabilization of time-delay systems

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artstein’s model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.     

Stability analysis for switched positive linear systems under state-dependent switching

This paper addresses the state-dependent stability problem of switched positive linear systems. Some exponential stability criteria are established on the given partitions of the nonnegative state space. First, a exponential stability of systems without delays is established with the help of a single linear co-positive Lyapunov function. When this does not seem possible, we also prove the stability by using multiple linear co-positive Lyapunov functions. Moreover, we extend this result to the delayed systems in terms of the single and multiple linear co-positive Lyapunov functionals respectively. The proposed results can be applied to the general systems without any special restriction. Some numerical examples are given to illustrate the effectiveness of our results.     

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.