On delay-dependent stability for a class of nonlinear stochastic delay-differential equations

Global asymptotic stability conditions for nonlinear stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov–Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of the system coefficients. Nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given.     

On the stochastic finite-time stability for switched stochastic nonlinear systems

In this paper, the stochastic finite-time stability (SFTS) criteria for switched stochastic nonlinear systems (SSNS) with nonlocal Lipschitz coefficients are established. The main tools that we used here are mode-dependent limiting average dwell time (MD-LADT), stopping time technology and the stochastic analysis theory. The established criteria show that the diffusion coefficient, the drift coefficient and the switching law play crucial roles in obtaining the SFTS for the SSNS. Besides, our criteria provide some approaches on how to design the switching law to achieve the SFTS if a switched stochastic system contains SFTS subsystems and stochastic finite-time instable (SFTI) subsystems simultaneously. Finally, an example is given to illustrate the importance and usefulness of the theoretical results.     

Robustness of stability of nonlinear systems with stochastic delay perturbations

Suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential-functional equation. In this paper a sufficient condition is given so that the perturbed system remains exponentially stable. In the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable.     

Novel delay-dependent stability condition for mixed delayed stochastic neural networks with leakage delay signals

In this paper, the problem of stability condition for mixed delayed stochastic neural networks with neutral delay and leakage delay is investigated. A novel Lyapunov functional is constructed with double and triple integral terms. New sufficient conditions are derived to guarantee the global asymptotic stability of the concerned neural network. This paper is more general than the paper by Zhu et al. [Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process. Lett. 41 (2015), pp. 1–27]. In our paper, we considered both the neutral delay and leakage delay, but the paper by Zhu et al. is not considering the neutral delay. Also we employed triple integrals in the Lyapunov functional which is not used in the paper by Zhu et al. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题. 运用Backstepping递推设计方法, 得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法.     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题，运用Backstepping递推设计方法，得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法。     

T-S模糊时滞系统的时滞相关鲁棒稳定新判据

研究了基于Takagi-Sugeno（T-S）模糊模型描述的非线性时滞系统的稳定性和H∞扰动抑制问题,利用线性矩阵不等式（LMI）技术,导出了一种满足优化H∞性能的时滞相关稳定新判据,该判据不仅适用于系统时滞变化率大于1的情形,且与现有方法相比具有更小的保守性,数值仿真结果证明了所提方法的有效性。     

Delay-range-dependent stability for uncertain stochastic systems with interval time-varying delay and nonlinear perturbations

This paper considers the problem of robust stability for a class of uncertain stochastic systems with interval time-varying delay under nonlinear perturbations. A new delay-dependent method for robust stability of the systems is proposed. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov–Krasovskii functional. The restriction used to bound some trace term in the existing methods is also removed. The resulting criterion derived from this method has advantages over previous ones in that it has less conservatism and enlarges the scope of application. The reduction in conservatism of the proposed criterion is attributed to a method to estimate the upper bound on the stochastic differential of the Lyapunov–Krasovskii functional without neglecting any useful terms in the delay-dependent stability analysis. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are provided to show the effectiveness and reduced conservatism of the proposed method.     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

一类时滞不确定随机系统的鲁棒控制的新方法

针对一类不确定含输入控制时滞的随机系统,提出了一种新的时滞相关鲁棒控制设计方法,利用线性状态变换、构造Lyapunov-Krasovskii泛函,在线性反馈控制律的作用下,获得了闭环系统依赖于时滞的稳定性条件.所得结论以线性矩阵不等式的形式表示.最后通过数值例子说明该方法的有效性.     

力反馈时延遥操作系统的时延相关稳定性分析

当力反馈双边控制系统的主从端之间存在时延时,系统的稳定性和透明性会遭到破坏.无源性方法能保证系统的时延无关稳定性,但由于稳定性和透明性冲突,系统的透明性较差.本文利用绝对稳定性理论推导出一种新的双边控制算法.它以时延相关稳定性代替时延无关稳定性作为控制设计的目标,牺牲一部分不必要的稳定裕度以改善系统的透明性.它在保证系统稳定性的前提下使系统具有更好的透明性,最后用仿真进行了验证.     

On delay-dependent stability conditions

It is quite common in stability analysis of time-delay systems to make a special transformation of the system under investigation in order to obtain stability conditions which depend on the values of the delays. In this note we discuss additional conditions for stability and robust stability of the transformed system which do not appear when the original system is considered.     

Improved stability and instability theorems for stochastic nonlinear systems

This paper focuses on sufficient conditions which make stochastic nonlinear systems stable and unstable. A series of new stability (instability) criteria, which admit the infinitesimal operator of Lyapunov (Lyapunov‐like or Chetaev) functions to be indefinite, are proposed using the uniformly asymptotically stable function. The obtained stability and instability theorems weaken the constraints on Lyapunov and Lyapunov‐like (or Chetaev) functions, respectively. Many existing classical stability and instability criteria can be regarded as special cases of the stability and instability results in this paper. Finally, the presented theoretical results are illustrated by some simulation examples.     

Mean square stability of stochastic Volterra integro-differential equations

The mean square stability of a non-linear stochastic Volterra integro-differential equation is studied. Non-convolution Volterra terms arise in both the drift and the dispersion term. Moreover, for the convolution case we determine the rate of convergence in terms of an integrability condition on the Volterra kernels.     

Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system. Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones. Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system. Finally, an example is given to illustrate the effectiveness of the proposed design approach.     

Theory and application of stability for stochastic reaction diffusion systems

So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.     

p-th moment exponential stability of stochastic differential equations with impulse effect

The p-th moment exponential stability of stochastic differential equations with impulse effect is addressed.By employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are established.In addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential stability.Several examples are also discussed to illustrate the effectiremess of the r...     

Output feedback for stochastic nonlinear systems with unmeasurable inverse dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.     

Stochastic input-to-state stability for impulsive switched stochastic nonlinear systems with multiple jumps

In this study, we investigate the stochastic input-to-state stability (SISS) of impulsive switched stochastic nonlinear systems. In this model, the impulse jumps are component multiple maps that depend on time. Thus the model differs from traditional impulsive systems with single impulse between two adjacent switching times. We provide sufficient conditions in three cases with the SISS system by using the Lyapunov function and average impulsive interval approach. The destabilising impulses cannot destroy the SISS properties if the impulses do not occur too frequently when all the subsystems that control the continuous dynamics are SISS. In other words, the average impulsive interval satisfies a lower bound restraint. Conversely, when all subsystems that control the continuous dynamics are not SISS, impulses can contribute to stabilising the system in the SISS sense when the average impulsive interval satisfies an upper bound. Then, we investigate the SISS property of impulsive switched stochastic nonlinear systems with some subsystems that are not SISS under certain conditions such that the property remains obtained. Finally, we show three examples to demonstrate the validity of the main result.