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.     

不确定时滞网络控制系统的状态反馈控制

在网络传输过程中, 系统的稳定性受不确定, 网络延迟, 丢包和错序所影响. 本文针对这些非理想网络状况,研究了网络控制系统状态反馈控制. 建立连续时间系统模型时, 还引入了一个定常状态时延, 使得模型更贴近实际.随后, 运用改进的Lyapunov-Krasovskii函数, 推导出网络控制系统鲁棒稳定的充分条件, 并基于该充分条件得到利用线性矩阵不等式(LMI)的控制器设计方法, 再运用迭代算法求解相关系数. 最后通过MATLAB数值仿真算例, 证明了本文方法的正确性和有效性.     

线性时滞系统的耗散控制

从全新的二次型供给率的耗散角度，研究了线性时滞系统的二次稳定性和耗散控制问题，给出了线性矩阵不等式(LMI)形式的充分条件。而且，考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题，同样给出了LMI形式的充分条件，并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。     

New iterative linear matrix inequality based procedure for H2 and H∞ state feedback control of continuous‐time polytopic systems

This article provides new linear matrix inequality (LMI) sufficient conditions for a generalized robust state feedback control synthesis problem for linear continuous‐time polytopic systems. This generalized problem includes the robust stability, H₂ ‐norm, and H_∞ ‐norm problems as special cases. Using a novel general separation result, which separates the state feedback gain from the Lyapunov matrix but with the state feedback gain synthesized from the slack variable, then allows the formulation of LMI sufficient conditions for the generalized problem. Compared to existing parameterized LMI based conditions, where auxiliary scalar parameters are introduced in order to include the quadratic stability conditions (ie, assuming a constant Lyapunov matrix) as a special case, the proposed new conditions are true LMIs and contain as a particular case the optimal quadratic stability solution. Utilizing any initial solution derived by the quadratic or some existing methods as a starting solution, we propose an algorithm based on an iterative procedure, which is recursively feasible in each update, to compute a sequence of nonincreasing upper bounds for the H₂ ‐norm and H_∞ ‐norm. In addition, if no feasible initial solution can be found for some uncertain systems using any existing methods, another algorithm is presented that offers the possibility of obtaining a robust stabilizing gain. Numerical examples from the literature demonstrate that our algorithms can provide less conservative results than existing methods, and they can also find feasible solutions where all other methods fail.     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

不确定离散模糊时滞系统的时滞相关H∞控制

研究了不确定离散T-S模糊时滞系统的稳定性分析与H∞控制问题．通过构造适当的Lyapunov泛函,给出了系统的时滞相关稳定新判据．进而利用线性矩阵不等式方法,研究了H∞模糊状态反馈控制器存在的充分条件,并提出控制器优化设计的迭代算法．     

具有多状态和控制时滞的控制系统的绝对稳定性分析

基于线性矩阵不等式方法, 对具有多个状态和控制的时变时滞的Lurie型控制系统的稳定性进行分析, 得到了系统绝对稳定的几个充分条件, 这些条件用线性矩阵不等式表示, 具有较低的保守性. 最后通过一个实例验证了所得条件的保守性较以往结果的保守性小.     

具有随机丢包的网络控制系统的镇定

研究具有随机丢包的网络控制系统(NCS)的镇定问题.同时考虑传感器节点到控制器节点(S/C)和控制器节点到执行器节点(C/A)的随机丢包,并分别对这两种丢包现象建模.基于Lyapunov稳定性理论,得到闭环系统全局均方渐近稳定的充分条件.进一步利用线性矩阵不等式(LMI)方法,得到状态反馈控制律的增益矩阵.数值仿真算例验证了所得结果的有效性.     

New results on strong practical stability and stabilization of discrete linear repetitive processes

Discrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. They arise in the modeling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a form of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and control law design algorithms for the strong practical stability property. Relative to alternatives, the LMIs for stability have a simpler structure and it is not required to impose particular structures on the matrix variables. These properties are extended to control law design, including those where state vector access is not required. Illustrative numerical simulation examples conclude the paper.     

基于分布式PID控制的任意阶线性多智能体系统的一致性

研究普通线性多智能体系统在有向拓扑结构下的一致性问题,提出一种基于分布式PID控制的新的一致性协议.\.首先通过变量转换将一致性问题转变为误差系统的渐近稳定问题;然后构造Lyapunov函数,基于线性矩阵不等式(LMI)给出系统实现一致性的充分条件;最后通过仿真与纯比例控制作了比较.仿真结果表明,系统的结构拓扑图在存在全局可达节点的条件下,通过选择合适的PID参数,可克服噪声的干扰,缩短系统的收敛时间.     

Robust stability and stabilization of discrete singular systems: an equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.     

Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay

In this note, we deal with the exponential stability and stabilization problems for quadratic discrete‐time systems with time delay. By using the quadratic Lyapunov function and a so called ‘Finsler's lemma', delay‐independent sufficient conditions for local stability and stabilization for quadratic discrete‐time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.     

基于LMI方法的保性能迭代学习算法设计

研究基于性能的迭代学习算法设计与优化问题.首先定义了迭代域二次型性能函数,然后针对线性离散系统给出了迭代域最优迭代学习算法;基于线性矩阵不等式(LMI)方法,针对不确定线性离散系统给出了保性能迭代学习算法及其优化方法.对于这两类迭代学习算法,只要调整性能函数中的权系数矩阵,便可很好地调整迭代学习收敛速度.另外,保性能迭代学习算法设计及优化过程,可利用MATLAB工具箱很方便地求解.     

Stability of neutral delay-differential systems with nonlinear perturbations

In this paper, the problem of the stability analysis for neutral delay-differential systems with nonlinear perturbations is investigated. Using the Lyapunov method, we present new sufficient conditions for the stability, in terms of the linear matrix inequality (LMI), which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.     

一类不确定模糊系统的二次稳定性的研究

利用T-S模糊模型对一类非线性连续不确定时滞系统进行建模,通过对时变时滞不确定T-S模糊系统基于状态反馈控制器二次稳定性问题的分析,给出了使系统二次稳定具有增益变化的模糊状态反馈控制器存在的充分条件,该充分条件以线性矩阵不等式的形式给出,因其所有参数都是线性的,所以具有数值易解性.设计实例表明了该设计方法的可行性和有效性.     

基于LMI的非线性摄动系统鲁棒绝对稳定性判据

讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄 动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性 条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据.     

UNKNOWN INPUTS OBSERVERS DESIGN FOR DELAY SYSTEMS

This paper concerns the design of functional, reduced and full order observers for linear time delay systems with unknown inputs. A new method generalizing those existing in the literature is presented for systems with unknown inputs, these unknown inputs are present in both the state and the measurement equations. Conditions for the existence of these observers are given and sufficient conditions for the stability independent of delays are derived using linear matrix‐inequality (LMI) formulation. The independent of internal delay and independent of delay cases are also presented. A numerical example is presented to illustrate our approach.     

积分二次约束线性系统的H∞控制器设计:一种LMI方法

基于动态耗散理论, 给出了具有积分二次约束线性系统稳定和具有L₂有限增益的充分条件. 导出了积分二次约束线性系统H_∞ 状态反馈和动态输出反馈降阶控制器的设计方法, 并转化为多个线性矩阵不等式, 利用LMI工具箱求解.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.