摄动离散Riccati方程解的上下界估计

讨论摄动离散Riccati方程正定解的估计问题。针对摄动参数满足范数有界不确定性情形,获得了正定解的上界和下界,且界的计算通过确定的离散Riccati方程的解给出,避免高阶代数方程的求解,同时得到基于Riccati方程的摄动离散系统稳定性分析的新方法,所给出的数值算例验证了方法的可行性。     

摄动离散矩阵Lyapunov方程解的估计

研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．     

离散代数Riccati方程解的上下界研究

研究离散时间代数Ｒｉｃｃａｔｉ方程（ＤＡＲＥ）给了了ＤＡＲＥ解的上界和下界估计人公式，所得结果与现有结果比较，具有较小的保守性，计算实例表明本方法的有效性。     

不确定性离散广义系统带有观测器的控制

利用带参数的李雅普诺夫函数，讨论了一类具有不确定性离散广义系统带有观测器控制的条件，参数的引进使设计具有灵活性。     

一类离散时滞切换系统的稳定性分析

对一类子系统含有离散时滞项的切换系统,研究了其渐近稳定的问题。通过引入一个矩阵,将受约束的二次型转换为不受约束的二次型,然后利用多Lyapunov函数法得出了这类切换系统渐近稳定的一个充分条件。最后通过一个仿真算例,验证了所得结论的正确性。     

一类不确定离散时间系统的鲁棒控制

本文针对一类离散时间不确定多输入系统,采用李雅普诺夫第二方法设计了一种鲁棒的线性状态反馈控制器.分析了控制系统的稳定性,并得出系统稳定的充分条件.最后给出仿真例子.     

求解矩阵方程的一种新方法

如果在矩阵方程中，矩阵A是稳定矩阵，则f(P)=‖PA＋A′P＋Q‖^2→minimun。最小。本文利用该原理解矩阵方程。     

一类离散时滞系统的复杂动力学行为研究

在混沌巨大潜在应用前景的推动下,混沌控制已经引起了学者们越来越浓厚的研究兴趣.混沌的一些特征参量为系统是否呈现混沌行为提供了直接的判断依据.针对一类离散时滞系统,研究系统动力学行为随时滞参数变化的情况.在得到系统有界的前提下,分析一类基于传染病传播机理的复杂网络模型,研究传染病的传播动力学行为随最大李雅普诺夫指数变化的情况.基于Wolf重构法,仿真出系统最大李雅普诺夫指数随着时滞参数变化的曲线图.当最大李雅普诺夫指数大于零,系统呈现混沌行为,传染病在有界区域内传播;反之,系统收敛,传染病则会慢慢的消失.     

线性离散时间系统分散估计的合成算法

本文给出了线性离散时间系统分散估计的合成算法。一个分散大系统的状态由多个子观测站进行量测,并由各自的局部处理器进行分散处理,给出系统状态的分散估计;然后合成器对分散估计进行合成处理,给出系统状态的整体估计。     

PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH TO STABILITY ANALYSIS AND DESIGN FOR POLYTOPIC SYSTEMS WITH INPUT SATURATION

This paper is devoted to stability analysis and synthesis of uncertain systems subject to input saturation. A new parameter‐dependent Lyapunov function analyzing approach is proposed to reduce the conservatism in stability analysis for the polytopic systems subject to input saturation. Some new stability conditions and a gain‐scheduling controller design method are then developed by the LMI optimization based approach. Numerical examples are used to demonstrate the effectiveness of the proposed design approach.     

STABILITY CONDITION OF DISTRIBUTED DELAY SYSTEMS BASED ON AN ANALYTIC SOLUTION TO LYAPUNOV FUNCTIONAL EQUATIONS

An analytic solution to Lyapunov functional equations for distributed delay systems is derived. The analytic solution is computed using a matrix exponential function, while conventional computation has been relied on numerical approximations. Based on the analytic solution, a necessary and sufficient stability condition for distributed delay systems with unknown but bounded constant delay is proposed.     

ON THE LYAPUNOV APPROACH TO ROBUST STABILIZATION OF UNCERTAIN NONLINEAR SYSTEMS

In the Lyapunov approach employed in this paper, known in the literature as Lyapunov control, or min-max control, robust, global uniform asymptotic stability is achieved by a discontinuous control law which ensures that the Lyapunov derivative is negative despite bounded uncertainty. For that, it is assumed that the uncertainties satisfy certain matching conditions, and that a Lyapunov function for the nominal plant is available. To obtain lower control magnitudes, this paper develops control laws which counter the uncertainties on a component-wise basis, rather than the usual normic one. Both the basic discontinuous control law, which is proved to provide robust global uniform asymptotic stability, and a continuous app roximation, which is proved to ensure global uniform ultimate boundedness, are derived. Application to model following is given. We adapt recent results on robust quadratic stabilization of nominally linear time-invariant plants subjected to nonlinear, bo unded and unmatched uncertain perturbations, to extend our results to this important class of systems; this is illustrated by two examples.     

SOME NEW ASPECT OF LYAPUNOV TYPE THEOREMS FOR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.     

非线性离散动态系统优化与参数估计集成的多模型方法

在非线性系统分时段线性化多模型基础上,给出了非线性离散动态系统优化与参数估计集成的多模型方法,并论证了算法的最优性和收敛性.在存在模型-实际差异的情况下,从分时段线性化多模型出发通过迭代运算可得到实际非线性离散动态系统的真实最优解.仿真结果表明了算法的有效性和实用性.     

ON ASYNCHRONOUS ITERATIVE METHODS FOR THE SOLUTION OF NON-LINEAR EQUATIONS AND SYSTEMS OF EQUATIONS FOR MULTIPROCESSORS

In this paper we investigate the problem of constructing iterative methods for solving non-linear algebraic equations and systems of equations, corresponding to a parallel implementation on a multiprocessor system with no synchronization between co-operating processes.     

ON TRANSITIVE SOLUTIONS OF $-FUZZY RELATION EQUATIONS DESCRIBING FUZZY SYSTEMS

The set of solutions of the $-fuzzy relation equation over finite spaces with values from linear lattice is considered. It is shown, that there exist solutions with various known types of the fuzzy transitivity, while the maximum solution has a special new type of so-called α-transitivity. An interesting convergence property of natural powers of the maximum solution is presented. That result and analogous ones, which hold for other types of transitive solutions, are applied for the analysis of the convergence of fuzzy systems described by $-fuzzy relation equations. In such a way, a new conceptual model for the behaviour of fuzzy systems is provided.     

内存不足的解决方法

本文在阐明了ＤＯＳ操作系统仍具有很强生产力以后，针对开发和使用ＤＯＳ应用程序出现的内存不足的问题，介绍了三种基本解决方法，并用一个实例说明了这些方法的实用性。     

关于一般耦合矩阵方程的迭代对称解

本文构造了一个有效的迭代方法(CGL)去求解一般耦合矩阵方程的对称解.若一般耦合矩阵方程关于对称解相容,则对于任意给定的初始对称矩阵组,利用所构造的迭代算法,都能在有限步迭代出所求问题的一组对称解,若选用一些特殊的初值,则可获得矩阵方程的极小范数对称解.最后的数值例子表明了所给算法的有效性.