Stability of multigroup‐coupled models by stochastic perturbations

This paper focuses on stability of multigroup‐coupled models by stochastic perturbation. Based on combining graph theory with stochastic differential equation, new methods are obtained, and sufficient conditions on pth moment exponentially stable and almost surely exponentially stable for the multigroup‐coupled models with stochastic perturbations are provided. These results are use for examining the stability of multigroup‐coupled models by stochastic perturbations. The results show that the random part plays an important role in the stability of the multigroup‐coupled models. It can be designed more easily in practice. At last, an example is worked out to demonstrate the effectiveness and advantage of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件,提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果,     

Mean-square stability of the Euler–Maruyama method for stochastic differential delay equations with jumps

This paper deals with the mean-square (MS) stability of the Euler–Maruyama method for stochastic differential delay equations (SDDEs) with jumps. First, the definition of the MS-stability of numerical methods for SDDEs with jumps is established, and then the sufficient condition of the MS-stability of the Euler–Maruyama method for SDDEs with jumps is derived, finally a class scalar test equation is simulated and the numerical experiments verify the results obtained from theory.     

Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays

In this paper, we investigate the adaptive output-feedback stabilisation for a class of stochastic non-linear systems with time-varying time delays. First, we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non-linear systems with time delays, and introduce a new stability notion and the related criterion. Then, for a class of stochastic non-linear systems with time-varying time delays, uncertain parameters in both drift and diffusion terms, and general constant virtual control coefficients, we present a systematic design procedure for a memoryless adaptive output-feedback control law by using the backstepping method. It is shown that under the control law based on a memoryless observer, the closed-loop equilibrium of interest is globally stable in probability, and moreover, the solution process can be regulated to the origin almost surely.     

pTH Moment Exponential Stability of Stochastic Partial Differential Equations with Poisson Jumps

In this paper, we study a class of stochastic partial differential equations with Poisson jumps, which is more realistic for establishing mathematical models since it has been widely applied in many fields. Under a reasonable condition, we not only establish the existence and uniqueness of the mild solution for the investigated system but also prove that it is pth moment exponentially stable by using the fixed point theory. Then, based on the well‐known Borel‐Cantelli lemma, further, we prove that the mild solution is almost surely pth moment exponentially stable. Our results improve and generalize those given in the previous literature, in particular, the Lyapunov direct method and successive approximation method. Finally, we give an example to illustrate the effectiveness of the obtained results.     

Robust stability and controllability of stochastic differential delay equations with Markovian switching

In this paper, we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with Markovian switching. Some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with Markovian switching.     

凸多面体不确定系统的符号稳定性分析

针对一类凸多面体描述的连续线性不确定系统研究其符号稳定性条件,从而从符号稳定的角度探索一种新的不确定系统鲁棒控制器设计方法.在矩阵符号稳定定义和必要条件的基础上,给出了矩阵集合符号稳定的定义和完整同源稳定符号型集合的概念,得到了凸多面体不确定系统符号稳定的充分必要条件.进一步分析了符号稳定凸多面体不确定系统的特征根分布与主对角线元素的关系,提出了基于符号稳定的不确定系统状态反馈镇定控制综合方法.相比于基于Lyapunov稳定性理论的不确定系统鲁棒控制方法,本文所提方法避免了求解线性矩阵不等式,并且更符合工程设计的习惯.通过一类三轴稳定卫星姿态控制问题的算例和仿真验证了所提方法的有效性.     

一类非线性不确定时滞系统的鲁棒镇定

基于Ｌｙａｐｕｎｏｖ稳定性理论,了一类具有状态非线性不确定线性时滞系统的鲁棒稳定的一个充分条件。通过求解一个代数Ｒｉｃｃａｔｉ方程即可获得鲁棒稳定控制器,并且该控制器不依赖于系统的时滞。具体算例说明了该方法有效性。     

Robust nonfragile guaranteed cost control for uncertain T-S fuzzy Markov jump systems with mode-dependent average dwell time and input constraint

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain Takagi-Sugeno fuzzy systems with Markov jump parameters, time-varying delay and input constraint. A nonfragile mode-dependent fuzzy controller with mode-dependent average dwell time (MDADT) is designed with input constraint. A sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.     

关联 Lurie 控制大系统的参数绝对稳定性

针对一类具有不确定性参数和参考输入的关联 Lurie 大系统, 研究其参数绝对稳定性的问题, 即同时考虑参数变化引起的平衡点的改变及其稳定性的问题. 首先, 基于分散状态反馈, 研究了当不确定性参数变化和参考输入改变时, 关联 Lurie 大系统参数稳定性存在条件和参数稳定区域. 其次, 给出了在该参数稳定区域中基于矩阵不等式条件的关联大系统稳定性存在的线性矩阵不等式 (LMI) 条件. 最后, 研究了多胞型关联 Lurie 大系统参数绝对稳定性存在的充分条件和求解算法. 仿真例子说明了方法的有效性.     

一类不确定时滞系统的鲁棒几乎干扰解耦问题

讨论了一类不确定时滞系统的具有稳定性的鲁棒H_∞ 几乎干扰解耦问题 (RADDPS), 利用线性矩阵不等式和代数Riccati方程方法分别得到了RADDPS可解的充分条件, 并且相应给出鲁棒静态状态反馈控制器的设计.     

Pole assignment for uncertain systems in a specified disk by statefeedback

This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the “quadratic d stabilizability” concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation     

Output regulation of time-varying systems

In this paper the output regulation problem for linear time-varying systems is considered. Replacing the regulator equation by a regulator differential equation we give a necessary and sufficient condition for the problem to be solvable. As in the time-invariant case we first solve the output regulation problem by state feedback and obtain the required condition. Then with the aid of observers we show that the same condition solves the general problem with measurement feedback. We then consider the classes of almost periodic and periodic systems and refine the main results. A simple example of an almost periodic system and simulation results are given to illustrate the theory.     

The almost sure asymptotic stability and pth moment asymptotic stability of nonlinear stochastic delay differential systems with polynomial growth

In this paper, we discuss the asymptotic stability of nonlinear stochastic delay differential systems (SDDSs) whose coefficients obey the polynomial growth condition. By applying some novel techniques, we establish some easily verifiable conditions under which such SDDSs are almost surely asymptotically stable and pth moment asymptotically stable. A nontrivial example is provided to illustrate the effectiveness of our results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Finite‐Time Stability and Stabilization of Linear Uncertain Time‐Delay Systems

Robust finite‐time stability and stabilization problems for a class of linear uncertain time‐delay systems are studied. The concept of finite‐time stability is extended to linear uncertain time‐delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite‐time stability of linear uncertain time‐delay systems is given. By virtue of the results on finite‐time stability, a memoryless state feedback controller that guarantees that the closed‐loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.     

非线性不确定系统的鲁棒镇定与HJI微分不等式

研究一类带模有界条件的非线性不确定系统的鲁棒镇定,定义了Ｌｙａｐｕｎｏｖ意义下的鲁棒镇定概念,得到了系统鲁棒镇定的充分必要条件。结果说明,在带模有界条件下,非线性不确定系统的鲁棒可镇定性与一个扩展的Ｈａｍｉｌｔｏｎ Ｊａｃｏｂｉ－Ｉｓａａｃｓ（ＨＪＩ）微分不等式是否存在正解完全等价。     

Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients

This paper investigates the adaptive state-feedback stabilization problem for a class of high-order stochastic non-linear systems with unknown lower and supper bounds for uncertain control coefficients. Under some weaker and reasonable assumptions, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution on [0,∞, the equilibrium of interest is globally stable in probability and the states can be regulated to the origin almost surely. A simulation example is given to show the systematic design and effectiveness of the controller.     

New criteria for stochastic suppression and stabilization of hybrid functional differential systems

This paper establishes new criteria for stochastic suppression and stabilization of hybrid functional differential systems with general 1‐sided polynomial growth condition. For an unstable nonlinear hybrid functional differential system with general 1‐sided polynomial growth condition, 2 independent Brownian noise processes are used to perturb the system into the stochastic hybrid differential system. Theoretical analysis shows that one of the nonlinear diffusion terms may suppress the explosive solution of deterministic system, and the other one can make the perturbed hybrid system almost surely stable with general decay rate.     

On almost sure stability of continuous-time Markov jump linear systems

In this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out.     

具有结构不确定性的输出反馈线性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。