线性时滞系统的相对稳定性分析方法

实际控制过程中,时滞的引入常常导致系统性能的下降,也使得系统的稳定性分析变得困难。从一类具有时滞项的线性时不变( LTI) 系统的特征根求解出发,研究了系统的稳定性分析问题。复平面上系统特征根的位置不仅决定了系统的绝对稳定性,还决定系统的相对稳定性-瞬态性能。由于时滞的引入,系统特征方程变成超越方程,其解的数量为无穷。并提出一种从超越方程实部和虚部系数中提取出双向量并结合二维向量旋转的解决方法,可以准确简洁地求出超越方程在复平面上指定区域边界上的根。最后给出仿真实例表明了算法的正确性和有效性。     

关联动态时滞系统的分散镇定

针对一类关联时滞系统,通过建立一个凸优化问题,提出一种具有较小反馈增益参数的分散稳定化控制器的设计方法,数值例子表明了该方法的有效性。     

具有滞后输入的不确定系统的鲁棒镇定

本文研究具有滞后输入的不确定系统的鲁棒镇定问题,导出了系统可以用一个无记忆状态反馈控制律鲁棒镇定的条件,据此,提出了一个鲁棒稳定化控制器的设计方法．     

一类线性离散时滞大系统的分散镇定

用一组线性矩阵不等式给出一类线性离散时滞大系统分散能镇定的一个充分条件,进而,通过建立和求解一个凸优化问题,提出了具有较反馈增益参数的分散稳定化状态反馈控制律的设计方法,所得到的控制器不仅使得闭环境系统是稳定的,而且还可以使得闭环系统状态具有给定的衰减度。     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

一类具有有界控制器的多重时变滞后系统的指数稳定性

考虑了一类具有多重时变滞后和有界控制器的不确定动力系统的鲁棒指数稳定性问题.匹配一个无记忆的控制器,确保存在一个吸收域.我们所考虑的这类系统的解收敛于一个给定的球.球的半径和指数收敛率可以任意选择.     

A note on the stability of fractional order systems

In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems.     

具有时滞的线性奇异系统镇定的Riccati方程方法

本文考虑了具时滞的线性奇异系统的镇定问题,利用Ｒｉｃｃａｔｉ方程方法给出了系统无记忆反馈控制器的设计,并得到了系统可经状态反馈镇定的条件。     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质,对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据,所得闭环随机大系统的和稳定性不依赖于任意实数滞后,并对不确定系数矩阵和随机扰动强度具有鲁棒性。     

Delay-dependent Stabilization Conditions of Controlled Positive Continuous-time Systems

The stabilization problem for a class of linear continuous-time systems with time-varying non differentiable delay is solved while imposing positivity in closed-loop. In particular, the synthesis of state-feedback controllers is studied by giving sufficient conditions in terms of linear matrix inequalities(LMIs). The obtained results are then extended to systems with non positive delay matrix by applying a memory controller. The effectiveness of the proposed method is shown by using numerical examples.     

Generalization of Tychonov''s Theorem with applications to adaptive control of SISO delay systems

This paper deals with single-input single-output delay systems with unknown transfer function parameters, including unknown, non-commensurate, real delays. A generalization of Tychonov's Theorem is obtained. This generalization is used to show the stability of a smooth adaptive controller when applied to a large class of delay systems. This paper generalizes the results in [1,2].     

相对阶的递推辨识

首先给出相对阶与输入一输出相关函数之间的关系，然后给出非线性时不变性控制系统的相对阶的递推辨识方法，并把结果扩展到多变量系统。     

基于LM I 方法的时滞分布参数控制系统的镇定

针对常时滞、多个常时滞及多个变时滞的分布参数控制系统,提出一种与现有研究分布参数控制系统不同的方法．该方法通过构造平均Lyapunov函数,利用LMI和矩阵不等式知识,在只要求系统本身所固有的系数是负定矩阵的条件下,给出了所研究的分布参数系统镇定的充分条件．当模型中时滞为常时滞时,所得的充分条件与时滞无关;当模型中时滞为变时滞时,所得模型的镇定准则依赖于时滞．此外,该方法一个显著优点是所获得的条件容易检验,因而易于应用．     

一类时滞矩形广义系统的镇定

为研究时滞矩形广义系统的镇定问题,首先引入时滞动态补偿器对系统进行反馈补偿,然后构建一个合适的Lyapunov-Krasovskii泛函,并选取先进的积分不等式来处理泛函导数的积分项,进而获得了以严格线性矩阵不等式(LMI)表示的时滞矩形广义系统的镇定条件。在此基础上,利用迭代线性矩阵不等式的算法计算动态补偿器和反馈增益的参数矩阵。最后,通过数值算例验证了方法的有效性和优越性。