平面系统稳定性的间接方法*

利用Routh 判据得到的间接检验矩阵特征值的方法讨论平面系统的稳定性问题,对于线性系统,该方法给出平面区间矩阵稳定性的充要条件.对于非线性系统,Jacobian 猜想的已知结果[5],该方法给出平面非线性系统稳定吸引域估计的一种算法.最后,该估计被利用于高维系统二维滑动模的设计.     

区间离散广义系统的鲁棒稳定性分析

讨论一类区间离散广义系统的鲁棒稳定性问题。在给出区间离散广义系统的等价描述之后,基于线性矩阵不等式,得到了问题的充要条件,数值例子说明了该方法的正确性。     

关于时变区间矩阵的稳定性研究

本文对无界时变区间矩阵Ｎ［ Ｐ（ｔ）,Ｑ（ｔ）］的稳定性进行了研究,给出了无界时 对变区间矩阵和具有分解的时变区间矩阵Ｎ［Ｐ（ｔ）,Ｑ（ｔ）］稳定的充分条件,推广和改进了文［１,２］的工作。     

离散区间系统的鲁棒稳定性分析

本文主要研究了离散区间系统的稳定性问题,以线性矩阵不等式的形式给出了离散区间系统鲁棒稳定性的充分条件,最后通过仿真验证了该方法是行之有效的。     

离散广义区间动力系统的稳定性

利用范数理论,研究离散广义区间动力系统的稳定性问题,给出其区间动力系统的正则、因果且稳定的充分条件.在此基础上,进一步考虑该系统的区间极点集的配置问题,给出了使离散广义区间动力系统的极点落在预先给定园盘内的判定定理.数值算例表明了该方法的可行性.     

动态区间系统的鲁棒稳定性

研究了动态连续间系统和离散区间系统的鲁棒稳定性问题,在给出了区间系统的一种等价描述之后,利用Lyapunov方法和RIccati方程方法,分别得到了连续间我系统和离散区间系统鲁棒稳定的充分条件,最后的数值例子说明本文的结果不仅保守性小,而且计算简单。     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和改进了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性．     

线性时变系统的区间稳定性和鲁棒稳定性

用矩阵测度研究了线性时变系统的区间稳 定性和具有非线性时变摄动的线性时变系统的鲁棒稳定性,得到了它们稳定的判别准则,所 得结果与文\[1~5\]的结果互不包含．     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

线性时变系统的稳定性

本文介绍线性时变系统方程解的估计问题。根据系统方程系数矩阵Ａ，给出一种方法找出方程解的上边界和下边界。而这种方法与方程的精确解是完全一致的。然后建立线性时变系统稳定性判据。     

Model Predictive Control of Nonlinear Discrete Time Systems with Guaranteed Stability

This paper presents the design of a new robust model predictive control algorithm for nonlinear systems represented by a linear model with unstructured uncertainty. The linear model is obtained by linearizing the nonlinear system at an operating point and the difference between the nonlinear and linear model is considered as a Lipschitz nonlinear function. The controller is designed for the linear model, which fulfills the stabilization condition for the nonlinear term. Unlike previous studies that have not considered a valid Lipschitz matrix of nonlinear term in the design process, we propose an algorithm in this paper in which it is considered. Therefore, the closed loop stability of the nonlinear system is guaranteed. A novel SOS optimization problem to determine design parameters is introduced, which leads to improved closed‐loop performance in comparison to a trial and error tuning procedure. Furthermore, an algorithm is presented to enlarge the region of attraction for the nonlinear closed‐loop system. Stability is improved by checking some additional conditions if which the system may be unstable if not considered. The validity of the proposed algorithm is confirmed by examples.     

Stability margin-based PD attitude control tuning for unstable flight vehicle

Proportional-derivative (PD) attitude control is widely used for the flight vehicles, especially in boost phase. Some of the flight dynamics are open-loop unstable, which often limits the achievable closed-loop performance. Based on the intrinsic characteristics of the linear model obtained from the small perturbation theory, simple numerical analytical tuning formulae of PD attitude control are derived to meet the gain and phase margin specifications. According to Routh stability criterion, the decreasing gain margin is obtained by using the approximation of delay amid low frequency with the established tuning rule. Some numerical polynomial solving approaches are employed to seek the feasible stability margin region, which is explicitly plotted in the 2-D plane. Taking engineering practice into account, the maximum gain constraint is also imposed. Finally, several numerical examples are presented to validate the analysis result.     

一种新的滑动模态到达条件

给出了确定滑动模态吸引区的新方法，用此方法讨论了控制受限情况下变结构控制系统的稳定性，研究了利用非线性切换函数设计的变结构控制系统。     

含有有色噪声的随机系统在适应稳定意义下的变结构控制

研究含吸典型环境随机噪声－Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｃｋｂｅｃｋ有色噪声的连续时间随机系统在实用稳定意义下的变结构控制,构造了变结构控制律,证明了滑动模的可达性,估计了系统运动达到滑动模的时间,证明了滑动模运动的实用稳定性和鲁棒性,文末用仿真实例验证了本文的结果。     

基于稳定性分析的一类欠驱动系统的滑模控制器设计

从稳定分析的角度提出了一种欠驱动系统的新型滑模控制方法．该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的．仿真实验进一步验证了该结论．     

On estimation of the domain of attraction for sliding mode control of underactuated nonlinear systems

A system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed‐loop system trajectory reaches the surface, it moves along the surface while converging to the origin. In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using sliding mode control in the presence of system uncertainties is presented. Specifically, it is shown that the closed‐loop system trajectories reach the sliding surface in finite time, and a constructive methodology to determine exponential stability of the closed‐loop system on the sliding surface is developed, which ensures asymptotic stability of the overall closed‐loop system. Furthermore, the aforementioned framework provides the basis to determine an estimate of the domain of attraction for the closed‐loop system with uncertainties. Finally, the results developed in the paper are experimentally validated using a linear inverted pendulum testbed to show a good match between the actual domain of attraction of the upward equilibrium state of the pendulum and its analytical estimate.Copyright © 2012 John Wiley & Sons, Ltd.     

不确定广义系统鲁棒区域稳定性

本文涉及广义线性系统的D－稳定性及不确定广义系统的鲁棒D－稳定性,其中D是线性矩阵不等式（LMI）来定义的且称为LMI稳定性区域,给出LMI形式的有关判据及用于计算机系统矩阵中不确定参量阵摄动“半径”的凸优化算法。     

单滞后区间动力系统的稳定性

本文研究如下单滞后时变区间动力系统ｘ（ｔ）＝Ｎ［Ｐ，Ｑ］ｘ（ｔ）＋Ｎ［Ｃ（ｔ），Ｄ（ｔ）］ｘ（ｔ－τ），τ≥０的渐近稳定性的ａ稳定性，给出了其渐近稳定和ａ稳定的充分条件，推广和改进了文［１，２］的工作。     

广义不确定系统的模糊滑模控制*

研究了广义不确定系统的模糊滑模控制问题。控制结构中采用模糊系统来补偿动态不确定性,利用李亚普诺夫理论,证明了闭环系统的所有状态是全局有界的。