Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities (LMI). Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

多模态It随机系统的均方稳定性与鲁棒镇定

研究由连续时间Markov链所确定的多模态It^o随机系统的均方稳定性与鲁棒镇定 ,得到了一般多模态It^o随机系统的k阶矩指数稳定性定理 ,线性不确定系统的均方稳定性定理 ,给出了线性不确定系统的鲁棒镇定控制器 .     

Stability and Stabilization of Two‐Dimensional LTI Switched Systems with Potentially Unstable Focus

This paper investigates stability and stabilization of two‐dimensional switched linear time‐invariant (LTI) systems with potentially unstable focus. For the case that the origin is a single common focus of all subsystems, we first give continuous positive definite functions related only to the elements of subsystems' state matrices. Then, based on the continuous positive definite functions obtained, this paper proposes several sufficient conditions of stability/asymptotic stability/instability of the kind of switched LTI systems. By means of the stability results proposed, global asymptotic stabilizing controls (GASC), global asymptotic stabilizing switching paths (GASSP) and corresponding algorithms are designed for two‐dimensional switched LTI systems with focus. Finally, two illustrative examples and numerical simulations demonstrate the effectiveness of the new stability and stabilization results obtained in this paper.     

Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays

In this paper, the problems of stability and stabilization for linear systems with time-varying delays and norm-bounded parameter uncertainties are considered. By constructing augmented Lyapunov functionals and utilizing auxiliary function-based integral inequalities, improved delay-dependent stability and stabilization criteria for guaranteeing the asymptotic stability of the system are proposed with the framework of linear matrix inequalities. Four numerical examples are included to show that the proposed results can reduce the conservatism of stability and stabilization criteria by comparing maximum delay bounds.     

Finite-time stability and stabilization of time-delay systems

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artstein’s model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.     

一类相似组合大系统的线性反馈镇定

研究相似组合大系统的二次镇定问题,利用系统的特殊结构导出其二次可稳的条件及（分散）状态反馈控制律律的求解方法,其特点是只需求解两个低阶Ｒｉｃｃａｔｉ方程或不等式,大大简化了控制器的设计。     

线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

Quadratic stability and stabilization of bimodal piecewise linear systems

This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained.     

时滞线性随机系统的均方稳定性与反馈镇定*

本文研究Ｉｔｏｏ型随机滞后系统的均方稳定性与反馈镇定。文中首先建立了Ｉｔｏ型随机滞后系统的新型稳定性定理，然后采用适当的Ｌｙａｐｕｎｏｖ泛函得到了时滞线性随机系统零解均方渐近稳定的一个充分性判据，该判据适用于完全滞后型的随机系统，据此判据，文中给出了时滞线性随机系统的滞后反馈镇定方法。     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

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.     

不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

Stabilization via dynamic output feedback for systems with output nonlinearities

The problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered. These systems are characterized by nonlinear terms, depending only on the ouputs. It is shown that for these systems stabilization via continuous state-feedback plus stabilization via output injection imply stabilization via continuous dynamic output-feedback. This generalizes a well-knwon result for linear systems.     

具输入饱和因子的广义系统的镇定

广义系统的镇定问题是广义系统理论的基本问题之一.为了研究具输入饱和因子 的广义系统的镇定,首先利用代数方法,借助大系统分解原理,对具输入饱和因子的广义系统 进行综合,给出闭环系统渐近稳定的判别条件.其次,给出了闭环系统E一渐近稳定的概念,利 用广义Lyapunov函数方法,研究具输入饱和因子的广义系统,提出了合适的反馈控制,得到 了具输入饱和因子的广义系统E一渐近稳定的判别定理.     

转移概率未知下具有双Markov 链的网络控制系统控制器设计

研究一类基于Markov模型的网络控制系统的稳定性和镇定控制器设计问题.针对网络控制系统中受控对象模型的随机切换和通信过程中的丢包问题,利用具有两个独立Markov链的离散时间Markov跳跃系统进行建模.在该Markov跳跃系统模态转移概率矩阵部分元素未知的情况下,充分考虑转移概率的约束条件,给出系统可镇定的充要条件和状态反馈控制器的设计方法.最后通过仿真示例验证了所提出方法的有效性.     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

Control Routh Array And Its Applications

In this paper the Routh stability criterion [16] has been developed into control Routh array. Some formulas for calculating the array are provided. Certain properties are investigated. Using it, the problem of stabilization of bilinear systems via constant controls is solved. Then by converting the problems, the method of control Routh array is also used to solve some other stability related problems, such as the stabilization of control systems, the stability of uncertain Hurwitz matrix and the stability of interval matrices. Several algorithms have been developed to provide numerical solutions.     

具有有界时滞的网络控制系统的镇定

针对具有有界时滞且时滞上界大于一个采样周期的网络控制系统,研究了系统建模和状态反馈镇定问题.在分析有界时滞的所有可能性的基础上,提出一种能够用于处理时变控制律问题的网络控制系统数学模型,进而将该系统的镇定问题转化为镇定一系列模型的鲁棒控制问题.根据 Lyapunov 方法,给出了保证闭环系统稳定的状态反馈控制器.仿真算例验证了所提出方法的有效性.     

一类切换系统极限环的反馈镇定研究

利用多Lyapunov函数法讨论一类切换系统极限环的反馈镇定问题．首先给出切换系统极限环的有界状态反馈、有界输出反馈以及动态反馈镇定定理；然后利用Jurdjevic—Quinn方法给出反馈控制器的具体形式，并证明了在给定反馈控制器的作用下，切换系统的极限环渐近稳定．仿真例子验证了结论的正确性．