一类混杂动态系统的能控性(Ⅰ)——基本结果

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成,第Ⅰ部分首先,提出含时滞的线性切换系统的数学模型,并介绍切换系统的基本概念—切换序列。其次,引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念,给出一些有关概念的基本性质,特别是分离引理。然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系,这个引理将在能控性的判定中起关键作用。这些概念和引理都将作为以后展开能控性分析所必需的研究工具。     

一类混杂动态系统的能控性(Ⅲ)——含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅲ部分,主要研究含多时滞的线性切换系统的能控性及其判定规则。首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。最后,研究时滞大小不一致的情形,指出能控性与时滞大小无关。     

一类混杂动态系统的能控性(Ⅱ)——含单时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含时滞的线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅱ部分,主要研究含单时滞的线性切换系统的能控性及其判定准则。首先给出周期型系统的单周期能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。     

若干类时滞切换系统的稳定性问题

主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.     

一类离散的时滞脉冲切换系统的H_∞二次稳定性

研究了一类离散的时滞脉冲切换系统的H_∞控制问题,利用Lyapunov稳定性理论和线性矩阵不等式方法,给出了离散脉冲切换系统具有性能指标γ的充分条件.     

粗糙线性空间

将粗糙集思想引入到线性空间。提出线性空间中子集的上近似和下近似的概念,给出上、下粗线性子空间与上、下粗不变子空间的概念,讨论粗糙集线性空间的有关性质。     

具有非对称通信时滞和切换拓扑的高阶多智能体系统的一致性

研究具有切换有向拓扑和非对称时变时滞的高阶多智能体系统的一致性问题.通过引入正交线性变换和Lyapunov-Krasovskii泛函方法,依据线性矩阵不等式给出了系统解决一致性问题的充分条件以及可容许时变时滞的上界估计.其主要贡献是基于Lyapunov方程和代数不等式建立了协议参数的显性设计,该参数设计形式简单且易于计算,并保证了所给充分条件中线性矩阵不等式的可解性,使得高阶多智能体系统的一致性在切换有向拓扑下对非对称时变时滞是鲁棒的.     

时滞广义时变系统的容许性分析与镇定

研究了时滞广义时变系统的容许性与镇定性问题.首先,基于广义Lyapunov不等式、线性矩阵不等式和受限等价方法,建立时滞广义时变系统的Lyapunov不等式,将时滞广义时变系统的容许性问题转化为求解时滞广义时变系统的Lyapunov不等式问题,得到了系统容许的充分条件.然后,根据充分条件进一步研究了时滞广义时变系统的镇定问题,给出了状态反馈镇定器的设计方法.最后,通过数值算例验证了所得结论的有效性.     

广义系统能控性的两个充要条件

能控性判定问题是现代控制论研究的重要课题,它是系统分析和设计的理论基础.本文给出了广义系统能控性的两个充要条件,该些结果也为判定广义系统的能控性提供了一些实用方法,最后给出了一个例子.     

线性控制系统对小时滞的鲁棒能控性

对于在Banach空间中线性控制系统对时滞的鲁棒能控性．给出一个充分条件,在这个条件下,证明对一个能控的线性系统施加某个小的时滞扰动之后,其能控性保持不变．     

非线性开关控制系统的能控性

本文研究了一类具有不同控制器的非线性开关控制系统的能控性问题.利用了几何控制的方法和Kalman秩条件,获得了这类控制系统的能控性结果,推广了E.Zuazua在参考文献[7]中的结论.     

一维抛物型系统切换控制下的近似能控性

考虑一维热传导方程在两个边界控制切换作用情形下的近似能控性.采用变分方法,通过某个二次泛函的极小值点构造合适的边界控制函数,使其满足切换条件,而且使得系统是近似能控的.     

Stability of Delayed Markovian Switching Stochastic Neutral-type Reaction-diffusion Neural Networks

This paper is concerned about exponential stability in mean square of Markovian switching delayed reaction-diffusion neutral-type stochastic neural networks (RNSNNs). By Lyapunov function method, several novel stability criteria on exponential mean square stability of Markovian switching RNSNNs with time-varying delays are obtained. In the end, two examples are given to verify the feasibility of our findings.     

On uniform exponential stability of linear switching system

We prove that the linear switching system , where is bounded valued square matrices and ?:[0,1,2,…)→Ω is an arbitrary switching signals, is uniformly exponentially stable if the sequence is bounded, where s(k) is bounded valued sequence.     

Modeling and Analysis of Modal Switching in Networked Transport Systems

We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system.     

Attractors synthesis for a Lotka-Volterra like system

The aim of this paper is to prove numerically, via computer graphic simulations, that the synthesis algorithmprovided by Danca et al. [1] can be utilized to synthesize any attractor of a dynamical system modeling a two-predator, one prey Lotka-Volterra like system. The algorithm switches in a periodic deterministic or a random way the control parameter inside a set of a chosen values. The obtained attractor is the same with the attractor obtained for parameter value taken as averaged value of the switched control values. This simple and effective algorithm relies on a convex property induced in the set of the attractors corresponding to the chosen switching parameters. The algorithm was tested successfully on systems depending linearly on the control parameter like Lorenz, Chen, Rossler, networks and other systems.     

Asymptotic Properties of Parabolic Systems for Null-Recurrent Switching Diffusions

This work is concerned with the asymptotic behavior of systems of parabolic equations arising fromnull-recurrent switching diffusions,which are diffusion processes modulated by continuous-time Markov chains.A sufficient condition for null recurrence is presented.Moreover,convergence rate of the solutions of systems ofhomogeneous parabolic equations under suitable conditions is established.Then a case study on verifying one ofthe conditions proposed is provided with the use of a two-state Markov chain.To verify the condition,boundaryvalue problems (BVPs) for parabolic systems are treated,which are not the usual two-point BVP type.Anextra condition in the interior is needed resulting in jump discontinuity of the derivative of the correspondingsolution.