变周期采样系统指数稳定的新条件

本文研究了线性采样系统在变周期采样下的指数稳定性问题.基于离散时间Lyapunov理论,构造了一个新的类Lyapunov泛函.该泛函不仅是时变的,还增加了对状态二次项的积分,而且不要求在采样区间内正定.利用这一新的类Lyapunov泛函,本文首先针对一类非线性采样系统提出了指数稳定性定理,再结合改进的Wirtinger积分不等式,导出了使变周期线性采样系统指数稳定以及渐近稳定的线性矩阵不等式条件.最后举例说明了所得稳定性结果比现存的某些文献报道的结果保守性较小.     

基于双边闭环Lyapunov泛函的采样控制系统稳定新判据

本文研究采样控制系统的稳定性问题.通过对采样区间进行分割处理,然后,充分利用分割后的状态信息,构造了新的双边闭环型Lyapunov泛函.在界定泛函导数的过程中,通过引入新建立的系统状态方程并应用自由矩阵积分不等式方法,获得了改进的采样控制系统稳定判据.由于这样的处理方式可以捕捉到更多采样控制系统的状态信息,因而可以有效地降低稳定性分析的保守性.最后通过两个经典的数值例子对得到的稳定判据进行验证.实验结果表明,相比现有的其他方法,本文方法所得到的结论具有更小的保守性.     

离散模糊系统分析与设计的模糊Lyapunov方法

研究离散T-S模糊控制系统基于模糊Lyapunov函数的稳定性分析及控制器设计问题.首先,构造出离散型模糊Lyapunov函数,模糊Lyapunov函数是系数与T-S模糊系统的模糊规则权重相对应的复合型Lyapunov函数.然后,得到了开环系统新的稳定性充分条件,与公共Lyapunov方法的结果相比,这一条件更为宽松.进而,基于一系列线性矩阵不等式设计出模糊控制器.最后,仿真实例说明了该方法的算法和本文条件的优越性.     

一类结构不确定采样系统的鲁棒控制

针对一类结构不确定性线性采样系统，在时域中用Lyapunov方法研究采样系统的鲁棒控制及最优鲁棒控制，给出了系统鲁棒稳定的充分条件以及相应的鲁棒控制律，控制律的求取借助于求解一类线性矩阵不等式（LMI），或求解满足特定线性不等式条件下的优化问题，算例结果表明，采样周期是一个关键性的设计参数。     

基于分段模糊Lyapunov函数的模糊系统稳定性分析和保性能设计

针对一类 Takagi-Sugeno (T-S) 连续模糊系统, 在分析模糊系统前提规则结构信息的基础上, 研究了其稳定性和保性能设计问题. 通过将模糊 Lyapunov 函数 (FLF) 和分段二次 Lyapunov 函数 (PQLF) 结合, 构造出分段模糊 Lyapunov 函数 (PFLF), 并提出了一种新的并行分配补偿 (PDC) 控制器. 基于 PFLF 方法, 得到了线性矩阵不等式 (LMI) 形式的模糊系统分析与设计的求解方法. 该方法继承了 FLF 与 PQLF 的优点. 仿真实例表明: 该方法所得稳定性判据更为宽松, 具有更好的保性能控制效果.     

离散广义系统稳定性分析与控制的Lyapunov方法

利用Lyapunov方法,研究离散广义系统稳定性分析与控制问题.得到了离散广义 系统正则、具有因果关系且渐近稳定的等价条件;还给出了相关的鲁棒稳定性分析与镇定方 法.     

一类不确定采样系统的鲁棒D控制研究

本文对一类范数有界不确定线性采样系统,提出了存在状态反馈控制律,使得闭环系统的所有极点均位于一给定的圆盘中且具有最优鲁棒H∞性能的一个充分条件。结合控制律反馈增益参数极小化的要求,建立一个具有线性矩阵不等式约束的凸优化问题,通过该问题的解决,可以构造一个具有较小反馈增益参数和给定要求的控制律,算例结果进一步表明,该控制器具有更好的扰动抑制性能。     

变时滞神经网络指数同步性的LMI新条件

研究了一类具有变时滞的非线性混沌神经网络的指数同步性问题。应用线性矩阵不等式和Lyapunov泛函方法,得到了具有驱动-响应结构的神经网络的指数同步性准则,建立了判断神经网络同步性的新的充分条件。通过实例说明了该方法的可行性和有效性。     

非线性采样系统指数稳定的新条件

研究了非线性采样系统的稳定性问题. 对以采样周期为参数的离散时间系统族, 证明了全局指数稳定的Lyapunov定理和逆定理. 分别基于系统的一般近似模型和Euler近似模型, 给出了闭环系统全局指数稳定的新条件. 与现有结果相比, 取消了Lyapunov函数全局Lipschitz连续的假设, 减弱了闭环系统全局指数稳定的充分条件.     

基于增广Lyapunov泛函的Lurie时滞系统的绝对稳定性

对Lurie时滞系统的绝对稳定性问题进行了研究. 利用增广的Lyapunov泛函结合自由权矩阵方法, 得到了系统基于线性矩阵不等式(LMI)的时滞相关绝对稳定条件. 数值实例表明本文方法所得结果要优于现有文献中的结果.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.     

Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling

This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.     

Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.     

Augmented Lyapunov functional approach for stability of neutral systems with mixed delays

This paper is concerned with the neutral‐delay‐dependent and discrete‐delay‐dependent stability for uncertain neutral systems with mixed delays and norm‐bounded uncertainties. Through constructing a new augmented Lyapunov‐Krasovskii functional and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay‐dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Lyapunov functional approach to robust stability analysis of continuous-time uncertain linear systems in polytopic domains

In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.     

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

This paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Input-output stability of sampled-data systems

The authors study the L_p input-output stability of a continuous-time controller, using the usual arrangement of periodic sampling and zero-order hold. It is noted that even if the hybrid system is exponentially stable, this arrangement does not yield L_p (1⩽p<∞) stability in general. It is shown that this problem can be alleviated if a strictly causal stable continuous-time filter (e.g. antialiasing filter) is introduced prior to the sampler. For various configurations, L _p stability is examined in connection with exponential stability     

On stability of linear neutral systems with mixed time delays: A discretized Lyapunov functional approach

This paper focuses on the stability problem for a class of linear neutral systems with mixed neutral and discrete delays. A discretized Lyapunov functional approach is developed for such kinds of systems. The resulting stability criteria are formulated in the form of a linear matrix inequality (LMI). These criteria are applicable to linear neutral systems with both small and non-small discrete delays. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservative. Numerical examples show significant improvement over approaches in the literature.