一类仿射非线性网络控制系统的稳定性分析

利用采样数字控制系统的方法分析了一类混杂动态系统模型描述的仿射非线性网络控制系统的稳定性问题.针对一类仿射非线性对象和线性数字控制器组成的网络控制系统,考虑了网络诱导延时对系统稳定性的影响,得到了仿射非线性网络控制系统一致渐近稳定的条件．仿真实例验证了理论分析的正确性．     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

An extended frequency-domain stability criterion for a class of sampled-data systems

A new frequency-domain stability criterion employing a Popov-type multiplier is obtained for a class of nonlinear sampled-data control systems containing a monotonically nondecreasing nonlinearity. This criterion is an extension of previous results, in that unlike other criteria of this type, no upper bound is placed on the derivative of the nonlinearity. An example is given in which this new criterion is used to obtain stability conditions for a non-linear sampled-data system. These conditions are less restrictive than those obtained using other stability criteria.     

变周期采样系统指数稳定的新条件

本文研究了线性采样系统在变周期采样下的指数稳定性问题.基于离散时间Lyapunov理论,构造了一个新的类Lyapunov泛函.该泛函不仅是时变的,还增加了对状态二次项的积分,而且不要求在采样区间内正定.利用这一新的类Lyapunov泛函,本文首先针对一类非线性采样系统提出了指数稳定性定理,再结合改进的Wirtinger积分不等式,导出了使变周期线性采样系统指数稳定以及渐近稳定的线性矩阵不等式条件.最后举例说明了所得稳定性结果比现存的某些文献报道的结果保守性较小.     

一类非线性状态时滞系统的基于采样控制器的渐近稳定问题

针对一类含有状态时滞的非线性系统,利用采样控制方法研究其渐近稳定问题.解决这一问题的关键在于对系统时滞的处理,以及对由于采样方法而产生的状态增长误差进行估计.由于所考虑的时滞是常时滞,可以利用分割方法对系统时滞进行分割,将时滞划分成与采样时间长度相同的数个时间区间,并基于这种分割,通过数学归纳法对系统状态增长误差进行估计.通过坐标变换引入一个比例增益压制系统的非线性项,然后设计含有比例增益的状态采样观测器和采样控制器,结合非线性时滞系统的Lyapunov泛函方法分析闭环系统的稳定性,最终确定比例增益和采样时间需要满足的条件,以保证闭环系统的渐近稳定性.最后通过数值例子表明所用研究方法以及所得研究结果是有效的.     

Robust sampled-data fuzzy control of nonlinear systems with parametric uncertainties: Its application to depth control of autonomous underwater vehicles

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi-Sugeno (T-S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.     

Uniform asymptotic stability of hybrid dynamical systems with delay

We formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a Lyapunov-Razumikhin technique. To demonstrate the developed theory, we conduct stability analyses for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

非线性时变时延系统的模糊采样最优控制

针对非线性时变时延系统,采用输入时延和自由权重矩阵方法研究模糊采样最优控制问题.应用T-S模糊系统表征非线性系统,控制器是零阶保持采样信号.由线性矩阵不等式给出最优控制准则,所设计的模糊采样控制器在闭环系统渐近稳定意义下可保证期望最优控制性能.最后,通过卡车拖车系统实验验证模糊采样控制设计方案的可行性.     

采样非线性系统的神经网络稳定自适应控制

针对一类动力学未知或难以建模的采样非线性系统,提出了一种基于神经网络的跟随控 制器稳定自适应控制方法.控制器采用径向基函数神经网络近似对象的动力学非线性,神经 网络参数的自适应规律由稳定理论得到.文中给出了系统稳定性和跟随误差收敛性的证明, 并通过仿真实例揭示了所提方法的性能.     

Stability theory of hybrid dynamical systems with time delay

By defining the bounded time lag space and other related concepts, this note formulates the notion of hybrid dynamical systems with time delay, which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis. It also investigates stability properties of invariant sets by the method of Lyapunov functions and the Razumihin techniques. Criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay. Those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled-data feedback control systems with time delay.     

On the absolute stability of sampled-data systems: The "Indirect control" case

A study is made of the problem of absolute stability or "Lur'e problem" in the case of a sampled-data control system containing one integrator in the loop. By the second method of Liapunov, a frequency-domain inequality is obtained which is shown to be a sufficient condition for the absolute stability of the class of systems under investigation. This inequality improves inequalities of similar type which have been obtained by means of the Popov approach.     

Formulas relating stability estimates of discrete-time and sampled-data nonlinear systems

We provide an explicit stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the estimate for the corresponding discrete-time system and a function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [[Reference to 1]] or extend some results in [[Reference to 4]] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.     

非线性采样系统指数稳定的新条件

研究了非线性采样系统的稳定性问题. 对以采样周期为参数的离散时间系统族, 证明了全局指数稳定的Lyapunov定理和逆定理. 分别基于系统的一般近似模型和Euler近似模型, 给出了闭环系统全局指数稳定的新条件. 与现有结果相比, 取消了Lyapunov函数全局Lipschitz连续的假设, 减弱了闭环系统全局指数稳定的充分条件.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

A training rule which guarantees finite-region stability for aclass of closed-loop neural-network control systems

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.     

A computational procedure to stabilize nonlinear sampled-data systems

In this paper, a sufficient condition for the stability of a class of nonlinear sampled-data systems, expressed in a matrix quadratic form, is derived. A programmed computational algorithm is constructed to implement the stabilization scheme. Application to third-order control problem is presented in order to demonstrate the developed procedure.     

切换非线性系统采样控制的研究现状与进展

切换非线性系统由于其广泛的工程应用背景以及重要的理论研究价值引起各行业学者的广泛关注.近年来,随着计算机技术的快速发展,切换非线性系统采样控制问题成为研究热点.对目前切换非线性系统采样控制领域的研究现状进行综述.首先介绍了切换非线性系统的基本问题,并梳理了切换非线性系统几个常用控制方法的基本思想.然后从时间触发采样控制和事件触发采样控制两个方面对切换非线性系统采样控制的国内外研究现状进行了论述.最后进行了总结并提出切换非线性系统采样控制领域未来值得关注的研究方向.     

基于采样控制的一类本质非线性系统的全局镇定

针对一类含不确定参数的本质非线性系统,基于非光滑控制技术,提出了 一种基于采样控制的全局非光滑镇定方案. 首先,基于加幂积分技术和递归设计方法,提出了一类采样状态反馈控制器构造性设计方法.然后,通过合理地构造Lyapunvo泛函,严格地证明了存在一个最大采样周期 可以保证闭环系统的全局渐近稳定性. 由于控制器是离散形式的,所以在实际中易于用计算机来实现. 仿真结果验证了该方法的有效 性.     

基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.