一类无限维随机关联大系统的全局指数稳定性

基于箱体理论,利用向量函数法,研究了一类无限维随机非线性关联大系统的全局指数稳定性.通过分析相应的随机微分不等式的稳定性,得到了该类大系统全局指数稳定的一个判据.该判据利用随机大系统的系数矩阵以及与大系统关联的Lyapunov矩阵方程的解构造判定条件来判定大系统的全局指数稳定性,计算简便,便于应用.     

New delay-range-dependent exponential estimates for singular systems with time-varying delay

This paper considers the problem of exponential stability for continuous-time singular systems with interval time-varying delay. By defining a novel Lyapunov-Krasovskii function and giving a tighter upper bound of its derivative, a new delay-range-dependent exponential admissibility criterion, which not only guarantees the regularity, absence of impulses and exponential stability of the system but also gives the estimates of decay rate and decay coefficient, is established in terms of linear matrix inequality (LMI). The resulting criterion has advantages over the result previously reported by Haidar et al. [17] in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Examples are provided to demonstrate the advantage of the proposed criterion.     

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

In this paper, the interconnecting structure between a certain system and its lower order subsystems within the infinite‐dimension stochastic interconnected systems is analyzed. Assuming that the excitations are parametric white noises, the exponential string stability for a few classes of nonlinear stochastic interconnected systems is discussed. By using the vector Lyapunov function method, the sufficient conditions of exponential string stability are derived, expanding the scope of the parameters for systems stability. Moreover, some cases of exponential string stability for vehicle‐following systems in automated highway systems are specified. Finally, an example is shown to illustrate the proposed method.     

Improved stability of a class of switched neutral systems via Lyapunov–Krasovskii functionals and an average dwell-time scheme

This article is concerned with the stability analysis for a class of switched neutral systems with mixed time-varying delays. The upper bound of derivative of the discrete time-varying delay is not restricted to one. A delay-dependent criterion of exponential stability under switching signals with an average dwell time is developed by employing free weighting matrices. The criterion is given in the form of linear matrix inequality. A state decay estimation for the switched system is explicitly given by considering the individual rate of decay of state for each subsystem. Two simulation examples are given to illustrate the effectiveness of the proposed method.     

Stability analysis of large-scale systems with stable and unstable subsystems

Sufficient conditions are given for both exponential and asymptotic stability of time-varying non-linear large-scale systems composed of stable and unstable subsystems. Sign-negative coupling among the subsystems, which can be of arbitrary order and interconnected in arbitrary fashion, is allowable. Under the conditions the required stability property of the overall system is implied by the stability properties of all its subsystems and global features of their interactions. The interactions can be expressed in terms of time-varying, sign-indefinite functions rather than only in terms of time-invariant positive definite functions. Three examples are worked out to illustrate application of- the results.     

Lotka-Volterra-like approach to large-scale systems stability

A new aggregation form of large-scale systems is proposed in this paper. It is of the ‘Lotka-Volterra’ type and appears natural for the generalized Lotka-Volterra large-scale (possibly time-varying) systems, which is shown in the paper. The Lotka-Volterra aggregation form yields a comparison system of the generalized Lotka-Volterra type, which is composed of a linear and a non-linear part. In addition this aggregation form leads to new stability conditions for time-varying large-scale systems, and enables an extension of Weissenberger's results on exponential stability domain estimates to the asymptotic stability domain estimate of time-varying systems. An advantageous feature of the system aggregation and stability analysis developed in the paper is the omission of requirements for (any particular, e.g. exponential) stability of disconnected subsystems.     

Stability analysis for linear delayed systems via an optimally dividing delay interval approach

This paper addresses the problem of stability for linear systems with time-varying delay. A novel augmented Lyapunov–Krasovskii functional is constructed by using the idea of optimally dividing the delay interval [0,τ(t)] into some variable sub-intervals and line integral technology. Using the novel augmented functional, the new delay-dependent stability criteria are proposed for linear systems with time-varying delay. The gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay. Two numerical examples are provided to verify the effectiveness of the proposed criteria.     

多区域时滞电力系统稳定判据的优化

在大规模互联电力系统进行全网动态分析与控制的过程中,通信时滞的存在易导致动力系统产生控制设备失效、系统性能恶化及失稳等现象.而现有时滞系统稳定判据的研究多基于Lyapunov分析方法,研究过程中需采用不等式放缩及构造Lyapunov泛函,使得稳定判据具有较高保守性,增加了系统的控制成本.针对这一问题,本文以多区域时滞电力系统为研究对象,通过引入Wirtinger不等式优化稳定判据推导过程和构造新的Lyapunov泛函两种方式,降低系统稳定判据的保守性.最后,利用典型的二阶时滞系统和两区域负荷频率控制系统,验证了本文算法的正确性和有效性.     

An improved stability test and stabilisation of linear time-varying systems governed by second-order vector differential equations

In this article, the problems of exponential stability analysis and stabilisation of linear time-varying systems described by a class of second-order vector differential equations are considered. Using bounding techniques on the trajectories of a linear time-varying system, the stability problem of the time-varying system is transformed to that of a time-invariant system and a new sufficient condition for the exponential stability is obtained. Moreover, the new criterion is proven to be superior to a test presented in the recent literature. Finally, the proposed criterion is applied to the exponential stabilisation problem via state feedback. The results are illustrated by several numerical examples.     

New delay-interval stability condition

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r,?τ]. The case of unstable delayed systems for r?=?0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.     

Control of a group of systems whose communication channels are assigned by a semi-Markov process

This technical note is concerned with the problem of medium access constraint for a group of networked systems. The scheduling of each subsystem is defined by a stochastic protocol, which can be modelled by a semi-Makov chain with a time-varying transition probability matrix. The resulting closed-loop nonlinear systems are a semi-Markovian jump system with delay. Sufficient conditions for exponential mean-square stability of the resulting closed-loop systems are derived via a Lyapunov–Krasovskii method. Based on the stability criterion, the controller gain of each subsystem is designed. A simulation example is used to demonstrate the effectiveness of proposed method.     

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

This paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

Gain scheduled L-two-L-infinity filtering for neutral systems with jumping and time-varying parameters

In this paper,global exponential stochastic stability based continuous gain-scheduled robust L-two-L-infinity filtering problem is studied for a class of stochastic neutral systems subject to time-vary...     

DECENTRALIZED STABILIZATION OF H FUZZY CONTROL FOR NONLINEAR MULTIPLE TIME‐DELAY INTERCONNECTED SYSTEMS

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling errors between nonlinear multiple time‐delay systems and fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the UUB (uniformly ultimately bounded) stability of nonlinear multiple time‐delay interconnected systems with disturbances. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time‐delay interconnected systems and the Hcontrol performance is achieved in the mean time.     

Stability analysis of fuzzy large-scale systems with time delays in interconnections

The stability problem of fuzzy large-scale systems with time delays in interconnections is considered in this paper. The fuzzy large-scale system consists of J interconnected subsystems, which are represented by Takagi-Sugeno (T-S) fuzzy models. The stability conditions are derived using the Lyapunov-Krasovskii functional approach. This condition is independent of time delay and does not need the solution of a Lyapunov equation or Riccati equation. A stabilization approach for the delayed fuzzy large-scale systems through fuzzy state feedback-based controller is also presented in this paper. Finally, an example is given to demonstrate the result.     

具有马氏跳跃参数的切削加工系统控制问题研究

以单刀具垂直切削加工系统为研究对象, 引入了变进给量控制方法, 建立了具有Markov跳跃参数的时变时滞跳跃系统模型. 通过对系统的随机稳定性分析, 给出了使系统呈均方意义下指数稳定的充分条件, 同时研究了在系统参数矩阵和状态转移率非精确可知情形下的鲁棒稳定性条件, 并讨论了时变时滞参数对系统状态变量指数衰减速率的影响关系. 最后以仿真算例说明了本文所提方案的有效性.     

Stability analysis for linear switched systems with time-varying delay.

This correspondence considers the stability problem for a class of linear switched systems with time-varying delay in the sense of Hurwitz convex combination. The bound of derivative of the time-varying delay can be an unknown constant. It is concluded that the stability result for linear switched systems still holds for such systems with time-varying delay under a certain delay bound. Moreover, the delay bound of guaranteeing system stability can be easily obtained based on linear matrix inequalities (LMIs). As a special case, when the time-varying delay becomes constant, the criterion obtained in this correspondence is less conservative than existing ones. The reason for less conservativeness is also explicitly explained in this correspondence. Simulation examples illustrate the effectiveness of the proposed method.     

Delay-varying repetitive control with application to a walking piezo actuator

The performance of systems that exhibit repetitive disturbances can be significantly improved using repetitive control. If the repetitive disturbance is periodic with respect to time, perfect asymptotic disturbance rejection can be achieved by well-known methods. However, many systems have a repetitive nature with respect to a variable other than time. For this type of systems, we propose a delay-varying repetitive control (DVRC) method, which employs a time-varying delay in the repetitive controller that is continuously adjusted based on the repetitive variable. An H_∞ norm-based criterion is derived that guarantees stability of the time-varying delay system for a given range of variations of the repetitive delay. The strengths of this new repetitive control scheme are shown by applying it to a nanomotion stage driven by a walking piezo actuator.     

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.