网络控制系统稳定性的图理论

针对具有有界时延和数据包丢失的网络控制系统,提出了一种新的稳定性判据.基于Lyapunov方法和图论理论,给出非线性离散和连续刚络控制系统渐近稳定的充分条件,获得保持这两类系统稳定的最大允许时延界.得到控制器设计方法.并且,利用区间矩阵的谱特征.给出网络控制系统区间稳定的充分条件.设计算法,获得比例积分反馈控制器增益.算例表明所提方法的有效性.     

基于观测器的非线性网络控制系统容错控制

研究了一类基于观测器的非线性连续网络控制系统容错控制器设计问题.针对传感器采用时间驱动方式,控制器和执行器均采用事件驱动方式的网络控制系统,设计了观测器,建立了基于状态观测器的增广闭环系统模型.利用线性矩阵不等式和自由权矩阵的方法,推导出闭环系统渐近稳定的充分条件,给出了观测器和容错控制器协同设计的方法.实例仿真证明了所用方法的有效性.     

不确定线性2-D离散系统的鲁棒滑模控制

针对不确定线性离散二维（2-D）系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.     

基于T-S模型的网络控制系统故障诊断

针对一类参数不确定并具有时延和丢包情况的非线性网络控制系统,为达到快速准确的进行故障诊断的目的,提出了一种基于T-S模糊模型的故障诊断方法.通过建立此系统的T-S模糊模型,利用平行分布补偿时延的思想设计了满足系统稳定性条件的状态反馈控制器,以及通过引入随机切换系统表示数据有无丢失情况下的基于模糊观测器的鲁棒故障诊断方法,然后基于 Lyapunov函数和线性矩阵不等式方法给出了该闭环网络控制系统渐近稳定的充分条件,最后通过仿真例子验证了该方法能够使闭环控制系统渐进稳定以及能够准确的进行故障诊断,验证了所设计方法的有效性.     

动态神经网络的输入2状态稳定性分析

针对非自治的动态神经网络系统，建立了动态神经网络的数学模型．并将其等效成一个非线性仿射控制系统．深入分析了该系统平衡点的存在性、唯一性和全局渐近稳定性，给出了系统输入-状态稳定的充分条件，构建了ISS-Lyapunov函数，并应用该函数确保了系统的全局渐近稳定性．     

空间多刚体系统姿态的协同控制

将一种针对多个一般非线性系统的基于输出反馈的协同控制方法应用在采用四元数法描述的空间多个刚体姿态的协同控制系统中去，给出了空间多刚体系统姿态协同控制问题有解的充分条件，并设计了多刚体系统姿态的协同控制律．算例仿真结果表明，此法设计的协同控制器能够稳定控制描述各个刚体系统的姿态四元数，使其渐近稳定．     

基于输入状态线性化的船舶直线航迹控制

针对船舶直线航迹控制系统的非线性数学模型,基于输入状态线性化技术,将状态变换和输入变换结合得到一个非线性反馈控制规律,并由得到的线性系统给出了非线性系统全局渐近稳定的充分条件.计算机仿真结果表明,该控制规律可以使船舶直线航迹控制全局渐近稳定,设计的控制律具有良好的控制效果.     

网络化时滞控制系统的有限时间稳定性分析

针对网络控制系统中存在于传感器-控制器-执行器间的双时延问题,提出了一种基于Markov模型的状态反馈控制策略.与传统应用Markov随机过程的方式相比,该策略采用两个Markov链描述每一个时延,通过状态反馈把该随机系统描述为具有四个随机参量的离散Markov跳变系统.利用Lyapunov有限时间稳定性理论分析得到该系统稳定的充分条件,并利用线性矩阵不等式(LMI)得到了可行的反馈矩阵.数值仿真结果进一步证明了该策略的有效性.     

一类船舶直线航迹控制系统全局渐近稳定的充分条件及推论

针对水面船舶直线航迹控制系统的非线性数学模型, 给出了一种使系统关系度为零的特殊重定义输出变量, 并得到了一类状态反馈控制律. 文中引入一种新的 Lyapunov 预选函数, 采用 Lyapunov 直接法研究系统的稳定性问题, 得到了系统全局渐近稳定的充分条件及推论. 数值仿真和模拟试验结果证明了该充分条件的正确性.     

非线性网络控制系统的故障检测

针对一类具有随机丢包的非线性网络控制系统,研究了系统的故障检测问题.基于T-S模糊模型将对象线性化,考虑了控制器和执行器之间、控制器和传感器之间的随机丢包现象,采用满足Bernoulli分布的二进制序列来描述数据传输的随机丢包.同时利用模糊主导子系统规则,设计了模糊观测器,给出了基于观测器闭环系统渐近稳定的充分条件,并通过数值仿真实验验证了该方法的有效性.     

一般2-D线性常系数离散状态空间模型渐近稳定性的一类Lyapunov方法

本文给出了一般2-D线性常系数离散状态空间模型(2-D GM)的渐近稳定性的定义以及相应的判据,并借助于Lyapunov方程给出了2-D Roesser Model(2-D RM)渐近稳定条件,推广和简化了文献[1,7]的有关结论。最后通过行列式的一个简单性质,证明了关于2-DGM渐近稳定性的判定可以转化为一类特殊的2-D RM的相应问题,从而得到了判定2-D GM渐近稳定性的Lyapunov方法。     

On a method for studying stability of nonlinear dynamic systems

A method for studying the stability of the equilibrium points of linearized, nonlinear dynamic systems of arbitrary order is considered. The method is based on the fact that, due to the nature of the mutual arrangement of the trajectories of the corresponding linearized system, and the boundaries of some simply-connected, bounded neighborhood of its equilibrium point, one can judge the asymptotic stability and instability of both this point and the equilibrium point of the nonlinear system. Necessary and sufficient conditions of asymptotic stability and sufficient conditions of instability of equilibrium points of linear systems are given. Together with the theorems of the first Lyapunov method, these conditions determine the sufficient conditions of asymptotic stability and instability of equilibrium points of nonlinear systems. In some cases, the proposed conditions may turn out to be preferable to the known ones.     

Regional stability of two‐dimensional nonlinear polynomial Fornasini‐Marchesini systems

This paper addresses the problem of regional stability analysis of 2‐dimensional nonlinear polynomial systems represented by the Fornasini‐Marchesini second state‐space model. A method based on a polynomial Lyapunov function is proposed to ensure local asymptotic stability and provide an estimate of the domain of attraction of the system zero equilibrium point. The proposed results that build on recursive algebraic representations of the polynomial vector function of the system dynamics and Lyapunov function are tailored via linear matrix inequalities that are required to be satisfied at the vertices of a given bounded convex polyhedral region of the state space. Numerical examples demonstrate the effectiveness of the proposed method.     

基于观测器的滑模控制非线性中立型时滞系统

针对一类状态不可测的非线性不确定中立型时滞系统,基于滑模控制理论,采用线性矩阵不等式的处理方法,提出了滑动模态鲁棒渐近稳定时滞相关的充分条件,设计了一类滑模观测器,同时给出了该观测器存在的充分条件;然后应用滑模控制的趋近率方法和基于观测器所得到的系统估计状态,综合了一类滑模控制器,该控制器同时保证了估计状态下滑模面和估计误差状态下滑模面的渐近可达性;最后通过数值实例证明了该控制方案的可行性.     

Stability analysis for delta operator systems subject to state saturation

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.     

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.     

Stabilisation of discrete 2D time switching systems by state feedback control

This article deals with sufficient conditions of asymptotic stability for discrete two-dimensional (2D) time switching systems represented by a model of Roesser type with state feedback control. This class of systems can correspond to 2D state space or 2D time space switching systems. This work is based on common and multiple Lyapunov functions. The results are presented in LMI form. Two examples are given to illustrate the results.     

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.     

On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term

Global asymptotic stability conditions for discrete vector nonlinear stochastic systems with state delay and Volterra diffusion term are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The derived stability conditions are directly expressed in terms of the system coefficients. A number of nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given. The obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems.     

Nonlinear Observer-based Control Design and Experimental Validation for Gasoline Engines with Exhaust Gas Recirculation

This paper presents a nonlinear observer-based control design approach for gasoline engines equipped with exhaust gas recirculation (EGR) system. A mean value engine model is designed for control which includes both the intake manifold and exhaust manifold dynamic focused on gas mass flows. Then, the nonlinear feedback controller based on the developed model is designed for the state tracking control, and the stability of the close loop system is guaranteed by a constructed Lyapunov function. Since the exhaust manifold pressure is usually unmeasurable in the production engines, a nonlinear observer-based feedback controller is proposed by using standard sensors equipped on the engine, and the asymptotic stability of the both observer dynamic system and control dynamic system are guaranteed with Lyapunov design assisted by the detail analysis of the model. The experimental validations show that the observer-based nonlinear feedback controller is able to regulate the intake pressure and exhaust pressure state to the desired values during both the steady-state and transient conditions quickly by only using the standard sensors.