CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME-DELAY CASE

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Research and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972≈), Doctor (E-mail:xiegming@mech.pku.edu.cn)     

索-梁组合结构主共振响应的时滞反馈控制

基于时滞加速度反馈控制策略对索-梁组合结构进行振动控制。根据Hamilton原理推导了索-梁组合结构非线性振动控制方程,运用多尺度法得到时滞反馈作用下索-梁组合结构主共振的一阶近似解,得出系统响应与控制参数的关系以及响应峰值和临界激励值与时滞参数的表达式。结果表明,主共振的响应存在多解和跳跃现象,调节控制增益和时滞值,可以有效抑制大幅振动。     

一类具时滞的广义区间系统的稳定性分析

讨论了一类具时滞的广义区间系统的鲁棒稳定性.利用一般的自治退化时滞微分系统的稳定性的V 泛函判别定理给出相应区间系统的V 泛函和稳定性的判据.     

状态和控制均含时滞的受外界扰动的线性系统的最优控制

主要研究一类受外界持续扰动且状态和控制含不同时滞的线性系统的最优控制,首先通过变量代换,将系统化为控制不含时滞的滞后型微分系统.接着使用最优控制的极大值原理的必要条件,得到含超前和滞后项的两点边值问题.为了得到最优控制律的解析解,引进一个灵敏参数ε,得到两点边值问题序列,通过迭代法,得到最优控制律的解析解.并对外界扰动状态构造降维观测器,来实现最优控制律的物理可实现性.最后实例验证了上述方法的有效性.     

Simultaneous output feedback stabilization of time-delay systems

^** Email: magdi_mahmoud{at}cic-cairo.com^*** Email: hnounou{at}uaeu.ac.ae This paper develops new results to the problem of simultaneousfeedback stabilization using static output feedback (SOF) controlfor a finite collection of linear dynamical systems with unknownstate delay. We establish tractable synthesis conditions fornominal SOF controllers and subsequently extend the resultsto resilient SOF to cope with possible additive controller gainperturbations. In both cases, the design of SOF controllersis based on guaranteed cost and approaches. Previous relatedresults are recovered and all the developed results are convenientlycast in the format of linear matrix inequalities. A numericalexample is presented.     

Delay-independent absolute stability for time-delay Lur'e systems with sector and slope restricted nonlinearities

This Letter presents an analysis method for a delay-independent absolute stability of time-delay Lur'e systems with sector and slope restrictions. The proposed method is based on the Lyapunov functions with quadratic form of states and nonlinear functions of the systems. Several criteria are derived in terms of linear matrix inequalities (LMIs). A numerical example is illustrated to show the effectiveness of the proposed method.     

An LMI-based approach for robust stabilization of time delay systems containing saturating actuators

Email: elhaous_fati{at}yahoo.fr Corresponding author. Email: elh_tissir{at}yahoo.fr Received on September 8, 2005; Accepted on July 24, 2006 This paper deals with the problem of robust stabilization foruncertain systems with input saturation and time delay in thestate. The parameter uncertainties are time-varying and unknownbut are norm bounded. Sufficient conditions obtained via a linearmatrix inequality formulation are stated to guarantee the localstabilization. The method of synthesis consists in determiningsimultaneously a state feedback control law and an associateddomain of safe admissible states for which the stability ofthe closed-loop system is guaranteed when control saturationseffectively occur. Numerical examples are used to demonstratethe effectiveness of the proposed design technique.     

LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback

In this paper, we propose a design method of an observer-based controller for uncertain time-delay systems by delayed feedback. Based on the Lyapunov method, an LMI (linear matrix inequality) criterion is derived to design an observer-based controller which makes the system stable. A numerical example is included to illustrate the design procedure.     

一类二阶时滞微分方程在控制系统中的应用

基于时滞微分方程稳定性理论,针对一类状态向量中含有时滞的控制系统,研究其时滞相关稳定性问题.通过构造Lyapunov函数,获得了系统稳定、分岔的时滞相关充分条件,所得结论推广和改进了某些已有文献的相应结果.且借助实例及仿真结果解释所得结果的有效性.