一类不确定时变时滞系统的鲁棒自适应稳定控制

研究了一类不确定时变时滞系统的鲁棒自适应稳定控制问题.系统包含多变时滞非线性扰动.基于Lyapunov稳定性理论和Lyapunov-K rasovsk ii型泛函设计出了一种无记忆的自适应状态反馈控制器,并证明了满足一定条件时,此控制器使得闭环系统最终一致有界.     

Energy decay of variable-coefficient wave equation with acoustic boundary conditions and delay

In this paper, we consider a variable-coefficient wave equation with memory type acoustic boundary conditions and a constant time delay in the boundary feedback. Using the Riemannian geometry method, we prove the exponential decay of the system with memory type acoustic boundary conditions and a constant time delay under some suitable assumptions.     

Complex Dynamics in a Hysteretic Relay Feedback System with Delay

Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.     

具有动态边界的非均匀Euler-Bernoulli梁的边界反馈镇定

本讨论一端带有重物的Euler-Bernoulli梁的边界反馈镇定问题。在生物的质量忽略不计而只考虑重物的转动惯量的情况下，证明了同时在梁的自由端施加力和力矩反馈，闭环系统的能量可被指数镇定。进而对于系统只有力反馈或只有力矩反馈的情况，得到了闭环系统（指数）稳定的充分必要条件。     

Stabilization of a type III thermoelastic Timoshenko system in the presence of a time‐distributed delay

In this paper, we investigate a Timoshenko‐type system of thermoelasticity of type III in the presence of a distributed delay. We prove the well‐posedness and two exponential stability results in the presence as well as in the absence of an extra frictional damping. In case of absence of the frictional damping, our stability result is obtained under the equal‐speed of propagation and a smallness condition on the weight of delay.     

Properties of stationary states of delay equations with large delay and applications to laser dynamics

We consider properties of periodic solutions of the differential‐delay system, which models a laser with optical feedback. In particular, we describe a set of multipliers for these solutions in the limit of large delay. As a preliminary result, we obtain conditions for stability of an equilibrium of a generic differential‐delay system with fixed large delay τ. We also show a connection between characteristic roots of the equilibrium and multipliers of the mapping obtained via the formal limit τ→∞. Copyright © 2004 John Wiley & Sons, Ltd.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control

In this paper, we consider a discrete delay logistic equation with feedback control. By applying the theory of difference inequality and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic sequence solution of the system are obtained. The result of this paper is completely new. An example is employed to illustrate our main result.     

具有时滞Michaelis-Menten型功能性反应的有放养的捕食链非自治扩散系统的一些性态

本文讨论了有放养的时滞Michaelis Menten型功能性反应的捕食链 .应用微分不等式和V函数法 ,在一定条件下讨论了该系统的一致持久性 ,得到了概周期解的存在唯一性及其全局吸引性 .     

Real-time calculation of current optimal feedbacks for a delay system

A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.     

Ecological complexity and feedback control in a prey–predator system with Holling type III functional response

This article deals with a bioeconomic model of prey–predator system with Holling type III functional response. The dynamical behavior of the system is extensively discussed. Continuous type gestational delay of predators is incorporated in the system to study delay induced instability. It is observed that the system undergoes singularity induced bifurcation at interior equilibrium point when net economic revenue of the system increases through zero. State feedback controller is designed to stabilize the system at positive economic profit. Time delay is considered as a bifurcation parameter to prove the occurrence of Hopf bifurcation phenomenon in the neighborhood of the coexisting equilibrium point. Finally, some numerical simulations are carried out to verify the analytical results and the system is analyzed through graphical illustrations. © 2015 Wiley Periodicals, Inc. Complexity 21: 346–360, 2016     

Finite spectrum assignment problem for a delay type system

For a spectrally controlled linear time-invariant delay system with commensurable delays, we construct a static state feedback ensuring an arbitrary finite spectrum of the closedloop system. By an appropriate choice of the spectrum, one can make the closed-loop system asymptotically stable. The results are illustrated by examples.     

Super-high-frequency oscillations in a discontinuous dynamic system with time delay

We study oscillations in the discontinuous dynamic system with time delay . This is a typical model of relay feedback with delay. It is known that stable modes in this system have a bounded oscillation frequency. Here we consider transient processes and obtain the following result: under some restrictions ofF, the average oscillation frequency of any solution becomes finite after a period of time, i.e. super-high-frequency oscillations (with infinite frequency) exist only in a finite time interval. Moreover, we give an effective upper bound on the length of this interval.     

带有反馈与起动故障的M/G/1重新访问排队系统的适定性分析

文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法.     

输入带有时滞的线性系统的镇定

考虑带有输入时滞的线性系统的镇定问题.通过把时滞写成一阶传播方程,带有输入时滞的镇定问题转化为常微分方程和一阶双曲方程组成的串联系统的镇定问题.与现有Backstepping方法不同,文章给出了新的变换,其核函数是一阶倒向向量值常微分方程,这使得控制的设计更加简单.文章给出了新的状态反馈控制器,并证明了闭环系统解的适定性和指数稳定性.数值模拟说明,给出的方法是非常有效的.     

半线性驱动-响应系统在输出反馈控制下的混沌同步

考虑一类半线性驱动一响应系统，提出了一种实用的输出反馈控制方法并研究了相应的同步条件，通过构造误差动力系统的二次Lyapunov函数并令其导数负定，证明了当非线性项对有界自变量有界且线性部分及输出矩阵也满足一定条件时存在反馈控制使系统同步．然后将主要结果推广至多变量情形．     

Asymptotics of the solution of a system with constant delay

We study a complicated linear homogeneous system with constant delay consisting of two subsystems, one of which contains an exponential factor multiplying the right-hand side. Under some conditions, we prove the existence of an asymptotically periodic solution of this system.     

Stabilization of a class of nonlinear composite stochastic systems

This paper deals with the stability for a class of nonlinear composite stochastic systems by feedback laws.Firstly,we give sufficient conditions for the existence of feedback laws which render the equilibrium solution of the stochastic system globally asymptotically stable in probability.Secondly,for stochastic systems of the same type,we prove that there exists a linear feedback law which exponentially stabilizes in mean square the closed–loop stochastic system at its equilibrium.     

Dynamic feedback control and exponential stabilization of a compound system

We studied the exponential stabilization problem of a compounded system composed of a flow equation and an Euler–Bernoulli beam, which is equivalent to a cantilever Euler–Bernoulli beam with a delay controller. We designed a dynamic feedback controller that stabilizes exponentially the system provided that the eigenvalues of the free system are not the zeros of controller. In this paper we described the design detail of the dynamic feedback controller and proved its stabilization property.     

On the stabilization of interconnected stochastic systems

The aim of this work is to prove that if the equilibrium solution of a nonlinear control stochastic system is locally asymptotically stable in probability by means of a continuous state feedback law, then the resulting stochastic system obtained by adding an integrator is also locally asymptotically stable in probability by means of a smooth, except possibly at the equilibrium solution, state feedback law. This result extends to the stabilization of stochastic systems a result proved by Tsinias [9] for deterministic systems. In our proof, we make use of the stochastic version of Artstein's theorem established in [4]