非线性滞后It(?)随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ito随机系统的滞后无关均方渐近稳定性,将关于线性时滞不等式的Halanay不等式推广到非线性情形,用Lyapunov函数和关于时滞随机系统的比较原理,得到了非线性滞后Ito随机系统滞后无关均方渐近稳定性的一些判据。     

Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control

Sufficient conditions are established for the global relative controllability of nonlinear system consisting of a bilinear mode with time-varying delays in control. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.     

Controllability of Singularly Perturbed Linear Time-Dependent Systems with Small State Delay

A singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two lower-dimension systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. The reduced-order and the boundary-layer systems are in separate time scales, and they do not contain the small parameter any more. Connections between the properties of controllability of these systems and such a property of the original system itself are established for all sufficiently small values of the parameter of singular perturbations.     

Predictive Compensation for Stochastic Time Delay in Network Control Systems

This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process, as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.     

Disturbance Decoupling of Time Delay Systems

A necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by a pure shift dynamic compensator. It corrects previously obtained results for multi‐input multi‐output (MIMO) systems. Also, necessary and sufficient conditions are given for the solvability of the problem by a dynamic compensator for single input single output (SISO) systems.     

State‐Feedback Stabilization of Stochastic Nonlinear Systems with Time‐Varying Delay and Different Orders

This paper studies the problem of state feedback stabilization for a class of stochastic time‐varying delay nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the backstepping design method and the adding of a power integrator technique, a state feedback controller is constructed to ensure the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is how to deal with the different power orders, time‐varying delay and the nonsmooth system perturbations. The efficiency of the state feedback controller is demonstrated by a simulation example.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

Robust Stochastic Stability for a Class of Singular Systems with Uncertain Markovian Jump and Time‐Varying Delay

This paper deals with the problem of the robust stochastic stability for a class of singular systems with uncertain Markovian jump and time‐varying delay. Sufficient conditions on the stochastic stability are presented. The obtained results are formulated in terms of strict linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed approaches.     

Controllability for Discrete Systems with a Finite Control Set

In this paper we consider the problem of controllability for a discrete linear control system x _k+1=Ax _k+Bu _k, u _k∈U, where (A,B) is controllable and U is a finite set. We prove the existence of a finite set U ensuring density for the reachable set from the origin under the necessary assumptions that the pair (A,B) is controllable and A has eigenvalues with modulus greater than or equal to 1. In the case of A only invertible we obtain density on compact sets. We also provide uniformity results with respect to the matrix A and the initial condition. In the one-dimensional case the matrix A reduces to a scalar λ and for λ>1 the reachable set R(0,U) from the origin is?

时滞系统的鲁棒稳定性分析

研究时滞系统的时滞独立稳定性和时滞相关稳定性问题。基于Ｂａｒｂａｌｅｔ引理,得到了一类检验线性时滞系统稳定性的简单条件。进一步研究了一类含非线性不确定性时滞系统的鲁棒稳定性问题。数值例子表明,所得到的结果比已有结果的保守性小。     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Robust Adaptive Control of Uncertain Stochastic Hamiltonian Systems with Time Varying Delay

This paper investigates the robust adaptive control problem for a class of time‐delay stochastic Hamiltonian systems. The system under study involves stochastics, parameter uncertaintiess, and time varying delay. The aim of this study is to design an uncertainty‐independent adaptive control law such that, for all admissible uncertainties, as well as stochastics, the closed‐loop Hamiltonian system is robustly asymptotically stable in mean square. Sufficient conditions are proposed to guarantee the rationality and validity of the proposed control laws, which are derived based on Lyapunov functional method. The performance of the controllers is validated through digital simulations.     

具有任意未知常时滞系统的鲁棒稳定性(英)

本文采用李雅普诺夫泛函法和一个矢量不等式建立了若干具有任意未知常时滞系统的鲁棒稳定性判据．所获得结果是时滞无关的、文中示例说明了所得稳定性判据减少了现存结果的保守性．     

非线性离散随机时变系统比例微分滤波

扩展卡尔曼滤波（EKF）是从极小化状态估计误差的方差得到的,没有考虑状态误差的变化率,因而对非线性时变系统EKF估计方法惯性作用 较大,从而产生估计滞后,提出了非线性离散随机系统比例微分滤波（PDF）,PDF联合考虑极小化状态估计误差和状态误差变化率的方差,克服了EKF对非线性时变系统估计滞后的缺点,估计具有适时性,提出了高估计的精度,仿真例子证明了所提出的估计方法的有效性。     

带时滞的线性时变奇异系统的稳定性

通过比较方法建立了一类带时滞的线性时变奇异系统的稳定性判据,并讨论了相应的带有时滞的时变区间奇异系统的稳定性,给出了一个稳定性的比较定理。     

非线性时延网络控制系统的模糊建模与控制

针对时变网络诱导时延小于一个采样周期的非线性时延网络控制系统,讨论系统的稳定性及控制器的设计方法.利用基于“IF-THEN”规则的模糊模型近似系统中的非线性,将时延的不确定性转化为系统参数的不确定性,从而将此类非线性网络控制系统建模为一类具有参数不确定性的离散Takagi-Sugeno（T-S）模糊模型.基于建立的模型,利用Lyapunov方法和线性矩阵不等式方法,分析了系统的稳定性及模糊状态反馈控制器的设计方法,最后通过仿真实例验证了所提出方法的有效性.     

Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay

This paper is concerned with the problem of delay‐dependent passive analysis and control for stochastic interval systems with interval time‐varying delay. The system matrices are assumed to be uncertain within given intervals, and the time delay is a time‐varying continuous function belonging to a given range. By the transformation of the interval uncertainty into the norm‐bounded uncertainty, partitioning the delay into two segments of equal length, and constructing an appropriate Lyapunov–Krasovskii functional in each segment of the delay interval, delay‐dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. The main contribution of this paper is that a tighter upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained via a newly‐proposed bounding condition. Based on the criteria obtained, a delay‐dependent passive controller is presented. The results are formulated in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the method.     

时滞Lipschitz非线性系统观测器设计

给出了满足Lipschitz条件的离散非线性时滞系统的全维、降维观测器的设计方法和误差收敛的充分条件,并分别进行了证明.全维观测器通过将带有非线性项的矩阵不等式转化为两步线性矩阵不等式解出两个增益矩阵.降维观测器则通过解线性矩阵不等式(LMI)方便地获得观测器的增益矩阵,消除了增益矩阵选取的盲目性.通过对同一模型的仿真分析,两种观测器的状态估计误差均能迅速收敛到0,表明了所提出方法的有效性.     

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

In this paper, the interconnecting structure between a certain system and its lower order subsystems within the infinite‐dimension stochastic interconnected systems is analyzed. Assuming that the excitations are parametric white noises, the exponential string stability for a few classes of nonlinear stochastic interconnected systems is discussed. By using the vector Lyapunov function method, the sufficient conditions of exponential string stability are derived, expanding the scope of the parameters for systems stability. Moreover, some cases of exponential string stability for vehicle‐following systems in automated highway systems are specified. Finally, an example is shown to illustrate the proposed method.