一类线性参数变化时滞系统的H_∞控制

研究一类线性参数变化时滞系统的 H∞ 控制问题。这类系统的状态空间矩阵是一些时变参数的仿射函数 ,而这些时变参数是可以实时测量的。以线性矩阵不等式的形式给出了存在依赖于参数的动态输出反馈 H∞ 控制器的充分条件。当满足这些条件时 ,基于线性矩阵不等式的解可以构造出一种依赖于参数的动态输出反馈 H∞ 控制器     

中立时滞LPV系统基于观测器的控制器设计

研究一类中立时滞线性参数变化系统的基于观测器的控制问题．呆用Lyapunov方法,提出了系统的时滞相关稳定性条件,设计了增益调度控制器和状态观测器．利用参数线性矩阵不等式,将控制器存在的充分条件转化为凸优化问题．最后通过数值仿真验证了所提出方法的可行性．     

一类线性参数变化时滞系统的H ∞控制

研究一类线性参数变化时滞系统的H∞控制。这类系统的状态空间矩阵是一些时变参数的仿射函数,而这些时变参数是可以实时测量的。以线性矩阵不等式的形式给出了存在依赖于参数的动态输出反馈H∞控制器的充分条件。当满足这些条件时,基于线性矩阵不等式的解可以构造出一种依赖于参数的动态输出反馈H∞控制。     

时滞LPV系统的H∞控制新方法

研究了具有随参数变化状态时滞的线性参数变化系统的H_∞控制问题,该系统的状态空间矩阵和时滞是实时可测且在闭集内变化的参数的确定函数.提出了一种新的依赖于参数的H_∞性能准则,该准则通过引入附加矩阵解除了系统矩阵与依赖于参数的Lyapunov函数之间的耦合而更易于数值实现.在此基础上设计了系统的H_∞状态反馈控制器,该控制器能够保证相对于所有能量有界的输入信号闭环系统满足给定的性能指标.采用线性矩阵不等式技术,将控制器存在的充分条件转化为凸优化问题.最后用数值仿真验证了所提出算法的可行性.     

一类分布式时滞LPV系统的鲁棒H∞滤波

研究一类同时具有分布式和离散型时滞的线性参数变化系统的鲁棒H∞滤波问题．基于参数线性矩阵不等式方法,推导了滤波误差系统渐近稳定和具有H∞扰动衰减水平γ的时滞相关充分条件．同时应用投影定理,通过引入附加矩阵变量,解除了系统矩阵与依赖于参数的Lyapunov函数矩阵之间的耦合,使所得到的条件更适合于滤波器的综合．推导了系统鲁棒H∞滤波器存在的充分条件,并将滤波器的设计转化为一组线性矩阵不等式的求解．数值实例证明了所提出设计方案的可行性．     

具有Neumann边界的分布参数切换系统反馈镇定

通过构造Lyapunov函数,利用线性矩阵不等式,对一类具有Neumann边界的分布参数切换系统给出了状态反馈镇定的充分条件。该条件用一组线性矩阵不等式表示,将分布参数切换系统状态反馈镇定问题转化为一组线性矩阵不等式的可行解问题,可借助Matlab中线性矩阵不等式工具箱求解,因而容易检验和应用。最后通过数值算例,验证所提出设计方法的有效性。     

基于参数摄动模型的航空发动机鲁棒弹性自适应控制

航空发动机特性随飞行条件和工作状态变化,在复杂工作环境中同时存在模型不确定性和控制器自身参数变化问题,很大程度上影响整个飞行包线的控制性能。为此,文章提出一种基于参数摄动模型的航空发动机鲁棒弹性自适应控制方法。其首先建立了航空发动机参数摄动结构化模型;然后针对被控对象模型的不确定性和控制器增益的摄动,利用李雅普诺夫稳定性（Lyapunov stability）理论和线性矩阵不等式约束,设计了增益摄动有界但上界未知时的鲁棒弹性自适应控制律,将控制器的设计问题转化为线性矩阵不等式的可行解问题,使控制器的设计仅依赖线性矩阵不等式解矩阵的存在性,并证明了算法的稳定性。在此基础上,文章对飞行包线内发动机不同工作状态进行控制仿真验证。结果显示,调节时间小于1.8 s,超调量小于5%,这表明所设计控制器具有良好的稳定性和控制性能。     

时滞LPV重复过程的H∞控制

将时滞线性参数变化(LPV)思想应用于重复过程,研究其H∞控制问题.基于参数依赖Lyapunov函数方法,给出了该重复过程的稳定性和控制器设计的充分条件;同时通过投影定理引入两个附加矩阵,解除了重复过程矩阵和依赖于参数的Lyapunov函数矩阵之间的耦合,使得到的条件便于求解.仿真实例表明了该设计方法的有效性.     

含状态时滞及执行器饱和不确定系统反馈镇定及L2增益分析

研究了具有控制饱和状态时滞不确定系统的L2控制问题,提出了状态反馈方法,利用Lyapunov函数可获得时滞相关的线性矩阵不等式.线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L2性能水平,该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性.采用线性矩阵不等式技术,将控制器存在的充分条件转化为凸优化问题.在此基础上设计了系统的状态反馈控制器,最后用数值仿真验证了所提出方法的可行性.     

具有时变时滞的离散切换系统基于观测器的H∞控制

利用多Lyapunov函数方法，研究一类具有时变时滞的线性离散切换系统基于观测器的H∞控制问题．通过设计对角分块形式的多Lyapunov函数矩阵．使切换律只依赖于观测状态．在基于观测器的切换反馈控制策略下,给出了系统实现H∞控制的充分条件，且条件可以表示为与时滞界相关的线性矩阵不等式（LMI）的形式．同时还给出了切换律、观测器和控制器的设计方案．最后用一个仿真例子表明了结论的有效性．     

Linear parameter-varying discrete time-delay systems: Stability and l 2-gain controllers

In this paper, we investigate a class of linear parameter-varying discrete time-delay (LPVDTD) systems where the state-space matrices depend on time-varying parameters and the delay is unknown but bounded. We treat both notions of quadratic stability based on a single quadratic Lyapunov function and affine quadratic stability using parameter-dependent Lyapunov functions. In both cases, we develop LMI-based results of stability testing for time-delay as well as delayless discrete-time systems. Then, we design state-feedback controllers which guarantee quadratic stability and an induced l ₂-norm bound. For the case of dynamic output feedback control, we use a parameter-independent quadratic Lyapunov-Krasovskii function to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Throughout the paper, complementary results for linear parameter-varying discrete (LPVD) systems without delay are presented.     

Stabilisation of time-varying linear systems via Lyapunov differential equations

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

LPV system analysis via quadratic separator for uncertain implicitsystems

This paper considers a class of linear systems containing time-varying parameters whose behavior is not known exactly. We assume that the parameters vary within known intervals and there are known bounds on their rates of variation. Our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations. We first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model. We then develop a tool, called the quadratic separator, for stability analysis of uncertain implicit systems. Using this tool, a sufficient stability condition is obtained for the original linear parameter-varying system. Moreover, we show that the stability condition obtained is equivalent to the existence of a Lyapunov function that depends on the parameters in a linear fractional manner. Finally, the computational aspects of the proposed stability conditions are addressed     

基于观测器的不确定时滞系统的鲁棒控制

研究不确定线性时滞系统的状态观测器和基于观测器的鲁棒控制器设计问题,其中不确定性是时变的、不要求满足匹配条件。通过构造增广系统,利用Ｌｙａｐｕｎｏｖ稳定性理论,获得了该不确定系统存在状态观测器和基于观测器的鲁棒控制器的充分条件,同时给出了相应的状态观测器和基于观测器的鲁棒控制器。所得结论推广并改进了已知的一些结果,并通过实例说明了其有效性。     

二阶离散线性时变系统的一种稳定性判据

本文对二阶离散线性时变稳定性问题进行了研究。在离散线性时变系统Lyapunov稳定理论的基础上，给出二阶离散线性时变系统稳定的充分条件。即系统系数满足系数冻结条件和系数变化条件。仿真验证了结论的正确性。     

Parameter-dependent state observer design for affine LPV systems

In this paper, the design of a parameter-dependent state observer that allows to estimate the state of an affine linear parameter-varying (LPV) system is investigated. The observer has the property of being parameter-dependent since the corresponding state space matrices are scheduled using an interpolation method. Moreover, the stability of the estimation error is based on the existence of an affine parameter-dependent Lyapunov function. The main contribution of this paper is that the problem of the observer design and the existence of such a Lyapunov function is interpreted as a flexible LMI feasibility condition. Some illustrative examples are presented at the end of this paper.     

Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function

In this paper, the problem of exponential stability and stabilization for a class of uncertain linear time-varying systems is considered. The system matrix belongs to a polytope and the time-varying parameter as well as its time derivative are bounded. Based on a time-varying version of Lyapunov stability theorem, new sufficient conditions for the exponential stability and stabilization via parameter dependent state feedback controllers (i.e., a gain scheduling controllers) are given. Using parameter dependent Lyapunov function, the conditions are formulated in terms of two linear matrix inequalities without introducing extra useless decision variables and hence are simply verified. The results are illustrated by numerical examples.     

离散线性时变系统稳定性研究

本文对离散线性时变系统的稳定性问题进行了研究。给出离散线性定常系统收敛速度的定义，基于离散线性时变系统Lyapunov稳定理论，给出离散线性时变系统稳定的充分条件，即系统系数满足系数冻结条件和系数变化条件。仿真验证了结论的正确性。