On the model-based networked control for singularly perturbed systems with nonlinear uncertainties

In this paper, the model-based networked control is addressed for a class of singularly perturbed control systems with nonlinear uncertainties. An approximate linear slow and fast control system of the plant, which can be obtained by omitting the nonlinear uncertainties, are used as a model to estimate the state behavior of the plant between transmission times. The stability of model-based networked control systems is investigated under the assumption that the controller/actuator is updated with the sensor information at constant time intervals. It is shown that there exists the allowable upper bound of the singular perturbation parameter such that the model-based networked control system is globally exponentially stable.     

离散奇异摄动系统稳定性分析

讨论了关于离散奇异摄动系统的摄动稳定性解析条件, 给出了离散奇异摄动系统两种模型下的摄动稳定性充要条件. 通过分析状态矩阵的结构特性, 得出了系统稳定所需要的状态矩阵形式和限制条件. 同时, 通过广义系统途径也得到了 2-D 离散奇异摄动 Roessor 模型稳定的充分条件.     

Stabilization bound of discrete two-time-scale systems

In this paper, the exact ε-bound problem in various types of discrete two-time-scale (TTS) system is considered. A set of stability criteria based on the frequency domain representation is derived. Two interesting examples are used to demonstrate the proposed scheme.     

An infinite ∍-bound stability criterion for a class of multiparameter singularly perturbed time-delay systems

This paper presents an adjustable singular perturbed parameter approach, which is based on the Lyapunov stability theorem, in the stability analysis of multi-parameter singularly perturbed time delay systems for all εi ∈(0, ∞). A numerical example is given to compare our new results with those in the literature.     

State feedback design for singularly perturbed system using unified approach

The state feedback design for singuhrly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency, of the design.     

Robust stabilization of singularly perturbed systems

We discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models. In [1], it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the ‘true’ system containing both fast and slow modes. This phenomenon was then expanded to include the case where the simplified system is strictly proper in [2]. The objectives of this note are threefold: (i) to show that, given any proper system and any stabilizing controller for it that is proper but not strictly proper, there exists a singular perturbation of the system that is destabilized by that controller, (ii) to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter, and (iii) to provide a characterization, in the same spirit as [3,4], of the set of all strictly proper controllers that stabilize a given proper plant. By combining these results, it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system.     

受扰奇异摄动时滞组合大系统的近似最优控制

研究一类受扰奇异摄动时滞组合大系统的近似最优控制问题．基于奇异摄动的快慢分解理论．将原组合大系统的最优控制问题分解为组合线性快优化子问题和降阶的受扰时滞组合慢优化子问题．通过采用前馈补偿方法抑制外部扰动,采用参数摄动法求解组合慢优化子问题,得到了系统的前馈反馈组合（FFCC）控制律．通过引入降维扰动观测器解决了FFCC律的物理可实现问题．仿真算例验证了所提出方法的有效性．     

Growth conditions for exponential stability of time-varying perturbed systems

In this paper, we derive some sufficient conditions for practical uniform exponential stability of time-varying perturbed systems based on Lyapunov techniques, whose dynamics are in general unbounded in time, in the sense that the solutions are uniform stable and converge to a small neighbourhood of the origin. Under quite general assumptions, we first present a new converse stability theorem for a large class of time-varying systems, which will be used to prove certain stability properties of nonlinear systems with perturbation. Therefore, a new Lyapunov function is presented that guarantees practical uniform exponential stability of perturbed systems. Furthermore, some illustrative examples are presented.     

不确定奇异摄动系统的变结构控制设计与稳定性分析

对一类不确定奇异摄动系统给出一个变结构控制设计方法,并分析了滑动模的动态品质.最后给出一设计实例.     

奇异摄动系统的极限解

本文在前人工作的基础上,利用广义函数理论讨论了一般形式下的奇异摄动系统E(ε)(?)=A(ε)x+B(ε)u在v→0~+时的极限解问题,得出了这一极限解存在的充要条件。     

Feedback Stabilization of Singularly Perturbed Systems Under Information Constraints

The quantized feedback control for a class of singularly perturbed systems is addressed, in which the controlled system and the controller are connected via a limited capacity communication channel. First, a proper coder–decoder pair is presented such that the transmission error decays to zero exponentially under information constraints. Then, a control law in terms of linear matrix inequalities is constructed to render the resulting closed‐loop system input‐to‐state stable with regard to the transmission error. Thus the asymptotic stability of the closed‐loop system is guaranteed. It is shown that the proposed method is simple and easy to operate. Moreover, an upper bound of the small perturbation parameter for the stability of systems can be explicitly estimated with a workable computational way. Finally, two examples are presented to show the effectiveness of the proposed method.     

线性奇异摄动系统的特征结构配置

本文利用奇异摄动系统快、慢时间尺度特性和组合控制方法,将线性定常奇异摄动系统的特征结构配置问题等价地转化为由慢、快变子系统各自的特征结构配置问题来解决、并在各阶精度上进行了近似结果的研究.     

时滞的不确定奇异摄动系统鲁棒稳定性研究

研究了带离散时滞和分布时滞的不确定奇异摄动系统的鲁棒稳定问题.首先采用广义系统模型方法,将所研究的系统转化为与之等价的广义系统;然后提出对应的Lyapunov-Krasovskii泛函,得到了时滞相关的鲁棒稳定性判据,并在此基础上给出了鲁棒控制器设计,结论以矩阵不等式形式给出;最后仿真算例说明了方法的有效性.     

基于时延的网络控制系统稳定性分析

在20世纪90年代网络控制系统问世了,它综合了计算机技术、通信技术和控制系统理论,是一个新生的控制发展理论课题,是现代工业生产发展的风向标,基于时延的网络控制系统稳定性的分析就显得至关重要。本文简单介绍了网络控制系统的定义和网络控制系统发展现状、存在的问题,研究了基于实验补偿和预测控制的网络控制系统,针对不同控制系统的时延进行了分析。     

基于MPC网络控制系统的设计与稳定性分析

针对网络延时的问题,本文提出了一种改进的模型预测控制方法.该方法是利用MPC(模型预测控制)预测的将来控制信号来补偿前向通道出现的延时或中断,同时用一个预测器来补偿反馈通道延时.文中描述了它们的控制特性并讨论了该网络控制系统的稳定性,并用实例仿真验证该方法的可行性和有效性.