Multiple Lyapunov(多重李雅普诺夫)研究综述
Multiple Lyapunov 多重李雅普诺夫 - Multiple Lyapunov-like functions and graph-theoretic tools are the primary apparatuses for our analysis. [1] Especially, we further improve the applicability of this synchronization criterion by using multiple Lyapunov-type functions. [2] Sufficient conditions are achieved by using a multiple Lyapunov–Krasovskii functional. [3] Furthermore, stringent transient and steady-state performance and a guaranteed non-weighted H ∞ performance are achieved with the aid of multiple Lyapunov-like functions. [4] Proofs in detail are accomplished by using multiple Lyapunov–Krasovskii functions. [5] Multiple Lyapunov-Krasovskii function with multiple integral functions allows us to obtain less conservative conditions for a networked control system to satisfy the disturbance attenuation criterion. [6] By employing the method of multiple Lyapunov-Krasovskii functionals and the uniformly exponentially stable function, some relaxed Krasovskii-type sufficient conditions ensuring the pISS/piISS of the addressed systems are developed. [7]多个类似 Lyapunov 的函数和图论工具是我们分析的主要工具。 [1] 特别是，我们通过使用多个 Lyapunov 型函数进一步提高了该同步准则的适用性。 [2] 通过使用多个 Lyapunov-Krasovskii 泛函来实现充分条件。 [3] 此外，借助多个 Lyapunov 类函数，实现了严格的瞬态和稳态性能以及保证的非加权 H ∞ 性能。 [4] 详细证明是通过使用多个 Lyapunov-Krasovskii 函数完成的。 [5] 具有多个积分函数的多个 Lyapunov-Krasovskii 函数使我们能够为网络化控制系统获得不太保守的条件，以满足扰动衰减准则。 [6] 通过采用多重Lyapunov-Krasovskii泛函和均匀指数稳定函数的方法，开发了一些确保所讨论系统的pISS / piISS的松弛Krasovskii型充分条件。 [7]
average dwell time 平均停留时间
In view of the transient behavior caused by controller switching, the global stability of the switched system is analyzed using the multiple Lyapunov function approach and average dwell time condition. [1] Under the average impulsive interval (AII) with the average dwell time (ADT) and the mode-dependent average impulsive interval (MDAII) with the mode-dependent average dwell time, by adopting multiple Lyapunov functional approach, the inequality analysis technique and pinning control strategy, the global exponential cluster synchronization conditions are achieved. [2] Considering asynchronous switching phenomenon, the mean-square asymptotic stability is analyzed by the aid of multiple Lyapunov functional method and average dwell time (ADT) method. [3] The multiple Lyapunov function method is adopted to guarantee the tracking performance with designed average dwell time. [4] Then, by using the average dwell time switching approach and constructing multiple Lyapunov functions, a sufficient condition of IO-FTS for the considered system is presented in the form of linear matrix inequalities (LMIs). [5] Firstly, we propose the exponential stability criterion for a type of SPNSs when all subsystems succumb to average dwell time (ADT) switching by employing multiple Lyapunov functions (MLFs). [6] Taking the asynchronous switching into account, we give a switching law with the average dwell time (ADT) guaranteeing the exponential stability with the针对控制器切换引起的暂态行为，采用多李雅普诺夫函数法和平均驻留时间条件分析切换系统的全局稳定性。 [1] 在平均脉冲间隔（AII）与平均停留时间（ADT）和模式相关平均脉冲间隔（MDAII）与模式相关平均停留时间下，采用多李雅普诺夫泛函方法、不等式分析技术和钉扎控制策略，实现了全局指数簇同步条件。 [2] nan [3] nan [4] nan [5] 首先，我们通过采用多个 Lyapunov 函数 (MLF) 为所有子系统屈服于平均驻留时间 (ADT) 切换时提出了一种 SPNS 的指数稳定性准则。 [6] nan [7] 首先，通过使用多重 Lyapunov 稳定性理论，我们证明了如果平均驻留时间低于某个正常数。 [8] 通过采用平均驻留时间（ADT）技术和多个Lyapunov函数，获得了保证滤波误差系统是有限时间有界且具有规定的扰动衰减性能的新条件。 [9] nan [10] 通过构造适当的多个 Lyapunov-Krasovskii 函数并应用平均停留时间方法，设计了切换律和相关的异步弹性控制器，以保证具有指定 <inline-formula> <tex- 的闭环系统的有限时间有界性。 math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> 性能指数。 [11] 基于一种新的有界最大平均停留时间（BMADT）切换方法，利用一种新颖的时变分段多重李雅普诺夫函数方法推导出指数稳定条件。 [12] 通过构造一种新颖的分段多重Lyapunov函数方法，首先建立了具有有界最大平均停留时间的切换T-S模糊系统的指数稳定条件。 [13] nan [14] nan [15] nan [16] nan [17] nan [18]
mode dependent average 模式相关平均值
For each case, stability conditions are derived using multiple Lyapunov functions and mode-dependent average dwell-time, and thus relax the conservatisms caused by common Lyapunov function and average dwell-time. [1] By constructing appropriate multiple Lyapunov functions and employing mode-dependent average dwell time (MDADT) approach, some sufficient conditions are given to ensure that the system is FTB and finite-time H ∞ controllable. [2] By using multiple Lyapunov functions and mode-dependent average dwell time, we provide a sufficient condition for the p th moment exponential stability with fast convergence rate for deterministic switched discrete-time stochastic systems with stable and unstable subsystems. [3] By using the multiple Lyapunov–Krasovskii functionals (MLKFs) method combined with the mode-dependent average dwell time of stable subsystems (MDADTSS) and the mode-dependent average dwell time of unstable subsystems (MDADTUS) method, SSDSs with unstable subsystems are analyzed, and several novel sufficient conditions for finite-time stability and p th moment exponential stability are given. [4] For each case, stability conditions are derived using multiple Lyapunov functions and mode-dependent average dwell-time, and thus relax the conservatisms caused by common Lyapunov function and average dwell-time. [5] Secondly, based on the Lie derivative and iteration technique, some sufficient conditions, which can guarantee that switched affine non-linear systems are finite-time bounded with a prescribed H ∞ performance, are derived by applying the mode-dependent average dwell time and the multiple Lyapunov functions. [6] By using multiple Lyapunov functionals (MLFs) method, mode-dependent average dwell times, and the total activating time length of MLFs, some stability criteria are explicitly obtained for SNDSs with SDIs. [7] By adopting extended mode-dependent average dwell-time switching laws and semi-time-dependent multiple Lyapunov-like functions, the improved stability criterion is deduced for switched time-delay systems comprising of both stable and unstable subsystems. [8] The delay-dependent stability criterion of the STDSs with mode-dependent average dwell time (MDADT) switching is developed via the multiple Lyapunov–Krasovskii functional approach. [9]对于每种情况，稳定性条件都是使用多个 Lyapunov 函数和与模式相关的平均停留时间得出的，从而放松了由常见的 Lyapunov 函数和平均停留时间引起的保守性。 [1] 通过构造合适的多重Lyapunov函数并采用模态相关平均停留时间（MDADT）方法，给出了保证系统FTB和有限时间H∞可控的充分条件。 [2] nan [3] nan [4] nan [5] 其次，基于李导数和迭代技术，一些充分条件，可以保证切换仿射非线性系统是有限时间有界的，具有给定的H ∞ 性能，是通过应用与模式相关的平均停留时间和多个 Lyapunov 函数得出的。 [6] 通过使用多 Lyapunov 泛函 (MLF) 方法、与模式相关的平均停留时间和 MLF 的总激活时间长度，明确获得了具有 SDI 的 SNDS 的一些稳定性标准。 [7] 通过采用扩展模式相关的平均停留时间切换律和半时间相关的多个类Lyapunov函数，推导了包含稳定子系统和不稳定子系统的切换时滞系统的改进稳定性判据。 [8] nan [9]
closed loop system 闭环系统
Based on the novel multiple Lyapunov-like function, the sufficient conditions for the closed loop system to be globally uniformly exponentially stable (GUES) are obtained with admissible edge-dependent switching signals. [1] By using multiple Lyapunov function and defuzzifying for MFDM, a new mode-dependent fuzzy controller is proposed to assure the boundedness of the closed-loop system and the desired tracking performance. [2] Then, by means of the multiple Lyapunov-Krasovskii functional method, the delay-dependent bounded real lemma is derived to guarantee the stability of closed-loop system. [3] Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. [4] Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H∞ performance of the closed-loop system are deduced. [5] By utilizing the multiple Lyapunov function method and the backstepping technique together with the prescribed performance bounds, an adaptive NN controller is established which can ensure that all the signals in the closed-loop system are bounded under a class of switching signals with average dwell time and the tracking error converges to the predefined bounds. [6] Furthermore, by using multiple Lyapunov functions, a sufficient condition is put forward to make sure the state bumpless transfer performance, input bumpless transfer performance and asymptotical stability for the closed-loop systems. [7] By proposing a state-dependent switching law and utilizing the multiple Lyapunov function technology, the criteria are presented to ensure the local asymptotic stability with an基于新颖的多重类李雅普诺夫函数，通过允许的边缘相关开关信号，获得了闭环系统全局均匀指数稳定（GUES）的充分条件。 [1] 通过使用多重Lyapunov函数并对MFDM进行去模糊化，提出了一种新的模态相关模糊控制器，以保证闭环系统的有界性和所需的跟踪性能。 [2] nan [3] nan [4] nan [5] nan [6] nan [7] 通过提出与状态相关的切换律并利用多李雅普诺夫函数技术，提出了用<inline-formula> <tex-math notation="LaTeX">$H_{\infty }$保证局部渐近稳定性的准则</tex-math></inline-formula> 闭环系统的性能水平。 [8]
finite time stability 有限时间稳定性
Based on the multiple Lyapunov function method, the closed-loop teleoperation system with these two control methods is proved to be bounded and finite-time stability. [1] Some new conditions via multiple Lyapunov functions are given for stochastic finite-time stability of nonlinear time-varying SDEs. [2] Based on the multiple Lyapunov function method, the closed-loop teleoperation system with these two control methods is proved to be bounded and finite-time stability. [3] In addition, multiple Lyapunov functions-based criteria on stochastic finite-time stability are presented, which further relax the constraint of the infinitesimal generator $\mathcal{L}V$. [4]基于多李雅普诺夫函数法，证明了采用这两种控制方法的闭环遥操作系统是有界和有限时间稳定性的。 [1] 通过多个Lyapunov函数给出了非线性时变SDE的随机有限时间稳定性的一些新条件。 [2] 基于多李雅普诺夫函数法，证明了采用这两种控制方法的闭环遥操作系统是有界和有限时间稳定性的。 [3] 此外，提出了多个基于 Lyapunov 函数的随机有限时间稳定性判据，进一步放宽了无穷小生成器 $\mathcal{L}V$ 的约束。 [4]
dependent average dwell 依赖平均停留时间
The passivity conditions of such systems are studied by adopting the transition-dependent average dwell time (TDADT) and multiple Lyapunov functions (MLFs). [1] To effectively guarantee the stability of the considered system with unstable subsystems and reduce conservatism of the stability criteria, admissible edge-dependent average dwell time (AED-ADT) is first utilized to restrict switching signals for the continuous-time SNNs, and multiple Lyapunov–Kravosikii functionals (LKFs) combining relaxed integral inequalities are employed to develop two novel less-conservative stability conditions. [2]通过采用与跃迁相关的平均停留时间（TDADT）和多李雅普诺夫函数（MLF）研究了此类系统的无源条件。 [1] 为了有效地保证所考虑的具有不稳定子系统的系统的稳定性并降低稳定性标准的保守性，首先使用允许的边缘相关平均停留时间（AED-ADT）来限制连续时间 SNN 的切换信号，以及多个 Lyapunov-结合松弛积分不等式的 Kravosikii 泛函 (LKF) 用于开发两种新的不太保守的稳定性条件。 [2]
dwell time switching
Combining the multiple Lyapunov functions (MLFs) approach and the persistent dwell time switching technique, new sufficient conditions are obtained for the globally uniformly asymptotical stability of filtering error systems. [1]结合多李雅普诺夫函数（MLFs）方法和持续停留时间切换技术，获得了滤波误差系统全局一致渐近稳定性的新充分条件。 [1]
Dependent Multiple Lyapunov
Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H∞ performance of the closed-loop system are deduced. [1] By adopting extended mode-dependent average dwell-time switching laws and semi-time-dependent multiple Lyapunov-like functions, the improved stability criterion is deduced for switched time-delay systems comprising of both stable and unstable subsystems. [2] By using the delay- and parameter-dependent multiple Lyapunov–Krasovskii functional approach, sufficient criteria on uniform H∞ finite-time stabilization via observer-based state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. [3]nan [1] 通过采用扩展模式相关的平均停留时间切换律和半时间相关的多个类Lyapunov函数，推导了包含稳定子系统和不稳定子系统的切换时滞系统的改进稳定性判据。 [2] 通过使用延迟和参数相关的多重 Lyapunov-Krasovskii 泛函方法，通过基于观察者的状态反馈，提出了关于均匀 H∞ 有限时间稳定的充分标准，以解决问题的可解决性，这可以通过以下可行性问题来解决线性矩阵不等式的术语。 [3]
Employing Multiple Lyapunov
Firstly, we propose the exponential stability criterion for a type of SPNSs when all subsystems succumb to average dwell time (ADT) switching by employing multiple Lyapunov functions (MLFs). [1] By employing multiple Lyapunov-like functions, criteria on GUAS and event-GUAS are established. [2]首先，我们通过采用多个 Lyapunov 函数 (MLF) 为所有子系统屈服于平均驻留时间 (ADT) 切换时提出了一种 SPNS 的指数稳定性准则。 [1] nan [2]
Proper Multiple Lyapunov
By constructing proper multiple Lyapunov–Krasovskii functions and applying average dwell time methods, a switching law and the relevant asynchronous resilient controller are designed to guarantee the finite-time boundedness of the closed-loop system with a specified通过构造适当的多个 Lyapunov-Krasovskii 函数并应用平均停留时间方法，设计了切换律和相关的异步弹性控制器，以保证具有指定 <inline-formula> <tex- 的闭环系统的有限时间有界性。 math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> 性能指数。 [1] 通过使用适当的多重李雅普诺夫函数，初步建立了有限时间分布式控制器存在的充分条件，并以线性矩阵不等式的形式提出了设计准则。 [2]
Piecewise Multiple Lyapunov
Based on a new bounded maximum average dwell time (BMADT) switching approach, an exponential stability condition is derived with a novel time-varying piecewise multiple Lyapunov function approach. [1] By constructing a novel piecewise multiple Lyapunov function approach, an exponential stability condition of switched T-S fuzzy systems is first established with the bounded maximum average dwell time. [2]基于一种新的有界最大平均停留时间（BMADT）切换方法，利用一种新颖的时变分段多重李雅普诺夫函数方法推导出指数稳定条件。 [1] 通过构造一种新颖的分段多重Lyapunov函数方法，首先建立了具有有界最大平均停留时间的切换T-S模糊系统的指数稳定条件。 [2]
Applying Multiple Lyapunov
First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. [1] Furthermore, by applying multiple Lyapunov functions and S-procedure theory, the observer design problem can be converted into the existence issue of the solutions to the linear matrix inequality. [2]Constructing Multiple Lyapunov
Then, by using the average dwell time switching approach and constructing multiple Lyapunov functions, a sufficient condition of IO-FTS for the considered system is presented in the form of linear matrix inequalities (LMIs). [1] By skillfully constructing multiple Lyapunov–Krasovskii functionals and successfully solving several troublesome obstacles, such as time-varying delay and switching signals and nonlinearity in the design procedure, the switched linear output-feedback controllers designed can render the resulting closed-loop switched system semi-globally stabilizable under a class of switching signals with average dwell time. [2]Traditional Multiple Lyapunov
Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and performance by incorporating the idea of AED–ADT. [1] This is not a simple extension of traditional multiple Lyapunov functions because of the introduction of external parameter and dwell time. [2]Novel Multiple Lyapunov 小说多重李雅普诺夫
Based on the novel multiple Lyapunov-like function, the sufficient conditions for the closed loop system to be globally uniformly exponentially stable (GUES) are obtained with admissible edge-dependent switching signals. [1] By constructing a novel multiple Lyapunov functional (MLF), a sufficient criterion formulated by linear programming (LP) is established for the FTBS and the estimation of the settling time. [2]基于新颖的多重类李雅普诺夫函数，通过允许的边缘相关开关信号，获得了闭环系统全局均匀指数稳定（GUES）的充分条件。 [1] 通过构造一个新颖的多重 Lyapunov 泛函 (MLF)，为 FTBS 和建立时间的估计建立了由线性规划 (LP) 制定的充分标准。 [2]
multiple lyapunov function 多重李雅普诺夫函数
In view of the transient behavior caused by controller switching, the global stability of the switched system is analyzed using the multiple Lyapunov function approach and average dwell time condition. [1] By using multiple Lyapunov function and defuzzifying for MFDM, a new mode-dependent fuzzy controller is proposed to assure the boundedness of the closed-loop system and the desired tracking performance. [2] We present sufficient conditions in terms of multiple Lyapunov functions for the origin of a class of hybrid systems to be finite-time stable. [3] For each case, stability conditions are derived using multiple Lyapunov functions and mode-dependent average dwell-time, and thus relax the conservatisms caused by common Lyapunov function and average dwell-time. [4] This is accomplished by generalizing Common Lyapunov Functions (CLF) and Multiple Lyapunov Functions (MLF) methods, the latter when applied to fractional switching systems (FSS) in the resetting. [5] In terms of multiple Lyapunov functions, a state-dependent switching law is designed to realize fault detection performance even if the robustness and fault sensitivity of each subsystem are local. [6] The sufficient conditions for the stochastic state-feedback incremental H ∞ control problem are obtained by solving a set of coupled iHJIs and by resorting to multiple Lyapunov functions. [7] For the longitudinal maneuver mission of air-breathing hypersonic vehicles, this paper develops an adaptive control strategy based on multiple Lyapunov function method. [8] The passivity conditions of such systems are studied by adopting the transition-dependent average dwell time (TDADT) and multiple Lyapunov functions (MLFs). [9] Based on the multiple Lyapunov function method, the closed-loop teleoperation system with these two control methods is proved to be bounded and finite-time stability. [10] Moreover, based on the method of multiple Lyapunov functions (MLFs) and the technique of adding a power integrator, a sufficient condition guaranteeing the solvability of the finite-time control problem for the system under consideration is derived via a designed switching law, where there is no subsystem whose corresponding control problem must be solvable. [11] When the cascade structure contains multiple controlled converter systems, the stability of the entire cascaded system is guaranteed by the superposition of multiple Lyapunov functions. [12] Then the switched PID adaptive controller is designed via error transformation and multiple Lyapunov function methods. [13] By the ergodic property of the semi-Markov process and the method of multiple Lyapunov functions, some sufficient conditions for almost sure exponential stability of stochastic systems are formulated, which cover some existing results in the literature. [14] The novel observer is designed using multiple Lyapunov functions based on L1-norm, reducing the estimation noise while increasing the accuracy. [15] Then, the stability of linear–nonlinear switching extended state observers (ESOs) is proved by multiple Lyapunov functions. [16] First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. [17] Some new conditions via multiple Lyapunov functions are given for stochastic finite-time stability of nonlinear time-varying SDEs. [18] This paper presents the development of a new set of switched velocity controllers of a swarm of unmanned ground vehicles (UGVs) from multiple Lyapunov functions, which are invoked according to a switching rule. [19] This function can be understood as a multiple Lyapunov function, consisting of an infinite number of partial Lyapunov functions, each of which is used for a certain time interval. [20] Then, by combining multiple Lyapunov functions with the initial state and acceptable state of B chi automata, a sufficient condition for the global exponential stability of the system with step decreasing Lyapunov functions is given. [21] Secondly, the stability criteria for cyclic switched linear (or nonlinear) systems with ACDT or both S-ACDT and U-ACDT are derived by resorting to a technique that uses multiple Lyapunov functions. [22] Closed-loop stability is shown to be guaranteed using the multiple Lyapunov functions theorem and the Barbalat’s lemma. [23] A common finite-time barrier function, multiple barrier functions and multiple Lyapunov functions are merged as a tool for analyzing the asymptotic stability of a switched nonlinear system under spatio-temporal specifications. [24] The main contribution of the study is the synthesis of a continuous-phase adaptive robust tracking control law for hybrid models of bipedal robotic walking by incorporating the construction of multiple Lyapunov functions into the control Lyapunov function. [25] Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. [26] By using the tools of multiple Lyapunov function and linear matrix inequality method, a neighbor-based distributed controller is designed for each following-agent so as to achieve (average) consensus tracking, even if the underlying switching communication network contains disconnected digraphs. [27] By applying the multiple Lyapunov function approach, sufficient conditions of exponential stability a. [28] Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and performance by incorporating the idea of AED–ADT. [29] The multiple Lyapunov function method is adopted to guarantee the tracking performance with designed average dwell time. [30] Then, by using the average dwell time switching approach and constructing multiple Lyapunov functions, a sufficient condition of IO-FTS for the considered system is presented in the form of linear matrix inequalities (LMIs). [31] Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the L∞ control performance of the event-triggered Markov closed-loop jump system. [32] These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. [33] With the aid of the multiple Lyapunov function method, constraints on switching signals are derived under which global fixed-time stability of zero solutions of considered systems can be guaranteed. [34] Firstly, we propose the exponential stability criterion for a type of SPNSs when all subsystems succumb to average dwell time (ADT) switching by employing multiple Lyapunov functions (MLFs). [35] On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve performance. [36] By utilizing the multiple Lyapunov function method and the backstepping technique together with the prescribed performance bounds, an adaptive NN controller is established which can ensure that all the signals in the closed-loop system are bounded under a class of switching signals with average dwell time and the tracking error converges to the predefined bounds. [37] By virtue of the multiple Lyapunov function technology and Newton-Leibniz formula, a sufficient condition is established to guarantee the exponential synchronization of switched cellular neural networks. [38] Taking the asynchronous switching into account, we give a switching law with the average dwell time (ADT) guaranteeing the exponential stability with the针对控制器切换引起的暂态行为，采用多李雅普诺夫函数法和平均驻留时间条件分析切换系统的全局稳定性。 [1] 通过使用多重Lyapunov函数并对MFDM进行去模糊化，提出了一种新的模态相关模糊控制器，以保证闭环系统的有界性和所需的跟踪性能。 [2] 我们提出了多个 Lyapunov 函数的充分条件，以使一类混合系统的起源是有限时间稳定的。 [3] 对于每种情况，稳定性条件都是使用多个 Lyapunov 函数和与模式相关的平均停留时间得出的，从而放松了由常见的 Lyapunov 函数和平均停留时间引起的保守性。 [4] 这是通过推广通用李雅普诺夫函数 (CLF) 和多李雅普诺夫函数 (MLF) 方法来实现的，后者在重置中应用于分数切换系统 (FSS)。 [5] 针对多个 Lyapunov 函数，设计了状态相关的切换律，即使每个子系统的鲁棒性和故障敏感性都是局部的，也能实现故障检测性能。