具有对称循环结构线性大系统的分散镇定特征

研究一类具有对称循环结构的连续和离散线性大系统的分散镇定特征,充分利用对称循环的特点,建立了判断这类系统可分散镇定的充分条件．在连续情形下,通过引进耦合结构模这一概念,揭示了这类系统分散镇定的重要特征,这就是当整个系统的耦合结构模给定之后,系统的分散镇定特性可以完全由各孤立子系统的结构所决定．这表明在这类系统的实际设计中,不管系统内中各子系统之间的耦合结构多么复杂,只要按一定的条件适当设计或修正各孤立子系统的结构参数,就能使所设计的大系统具有分散镇定特征,并提供了相应的分散镇定算法．对离散情形也进行了讨论,结果表明,连续系统与离散系统的分散镇定特征有着很大的差异．     

Vandermonde矩阵的逆模与大系统的分散镇定性

本文首先给出一种计算Ｖａｎｄｅｒｍｏｎｄｅ矩阵逆模的简单方法，并利用其计算结果对线性定常大系统的分散镇定性进行分析，得到了一个使大系统分散镇定的充分条件及相应的镇定算法同传统的方法相比，我们不仅考虑了关联矩阵的结构，也同时考虑了它的模，且容易计算，便题分析表明本文提供的判断方法具有较少的保守性。     

不确定二阶时变系统的稳定鲁棒性(英文)

首先基于系数矩阵的一致对称正定性建立了二阶线性时变系统稳定性的一个判据.该判据简单、明了,是作者早期给出的关于定常二节线性系统稳定性判据的直接推广.基于这一判据,文章进一步给出了具有参数不确定性的二阶线性时变系统的鲁棒稳定性.所得结果对于处理确定性二阶线性时变系统镇定问题和不确定性二阶线性时变系统的鲁棒镇定问题提供了便捷而有效的工具.最后,文章将提出的方法应用到某卫星姿态系统的控制中.     

实轮换对称型及其半正定性判定的可读证明

可读证明是不等式机器证明领域中的热点问题.针对具有对称零点的实轮换对称型,文章提出了其线性空间的一组基以及分拆算法和两种分拆形式用于对不等式进行可读证明研究.讨论了该线性空间的维数,以及轮换对称型半正定性的判别方法.给出了一类具有对称零点的轮换对称型的半正定性判定条件.大量实例表明此分拆方式在轮换对称型半正定性的判定及可读证明上具有很好的实用性.     

判别正定矩阵的一种算法

通过合同变换,ｎ阶实对称矩阵的正定性可以由（ｎ－１）阶实对称矩阵的正定性来确定,由此,文中给出了判别正定矩阵的一种算法。     

关于线性系统解的对称性算法的强稳定性的探索

关于线性方程解的算法方面,本文在对称非奇异矩阵类和对称正定矩阵类上给出了强稳定性算法.     

奇异摄动系统的一致稳定和镇定（英文）

针对一类线性时不变奇异摄动系统,研究其在稳定和镇定性方面关于小参数的一致性问题.当小参数处于有界而非闭区间时,将奇异摄动系统视为参数系统.同时,进一步地讨论该系统对小参数的依赖性.最后,利用线性矩阵不等式方法,给出了系统关于小参数具有一致性的稳定和镇定条件.     

三元对称形式的Schur分拆与不等式的可读证明

本文给出了一类三元对称形式(即对称齐次多项式)的一种分拆法,即将此类多项式表示成一类特定形式的正半定对称形式的线性组合,介绍分拆算法．并由此而给出了三元对称形式半正定的一个充分条件．     

求解一类分块二阶线性方程组的QHSS迭代方法

本文将QHSS迭代方法运用于求解一类分块二阶线性方程组. 通过适当地放宽QHSS迭代方法的收敛性条件,我们给出了用QHSS迭代方法求解一类分块二阶线性方程组的具体迭代格式,并证明了当系数矩阵中的(1,1)块对称半正定时该QHSS迭代方法的收敛性.我们还用数值实验验证了QHSS迭代方法的可行性和有效性.     

Markovian跳变不确定时滞分布参数系统的鲁棒控制

基于线性矩阵不等式方法对一类含Markovian跳变的不确定时滞分布参数系统的鲁棒控制进行了研究.通过构造恰当的Lyapunov泛函,计算弱无穷小算子,以一组线性矩阵不等式给出系统鲁棒镇定的充分条件.该充分条件易通过Matlab进行求解,方便实际应用.最后,数值例子验证了方法的有效性.     

Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections

The problem of the decentralized stabilization of a class of large-scale nonlinear and linear systems including time-varying delays in the interconnections is considered. By combining the Razumikhin-type theorem with the Lyapunov stability theory, we propose a class of decentralized state feedback controllers which can guarantee always some type of stability of large-scale time-delay systems. In this paper, we assume that the time-varying delays are continuous and bounded nonnegative functions. Furthermore, since the proposed decentralized state feedback controllers are independent of the delays, the results obtained in this paper are applicable to systems without exact knowledge of the delays, i.e., systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Controllability and observability of coordinated linear systems

This paper develops concepts of controllability and observability for the class of coordinated linear systems, a special class of linear hierarchical systems with a top-to-bottom information structure. The usual concepts of reachability and indistinguishability for linear systems are refined, taking into account the decentralized nature of coordinated linear systems. The corresponding controllability and observability decompositions are derived, and several concepts of controllability and observability for coordinated linear systems are introduced and discussed. These results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state-measurement and the second utilizes static output-feedback. The decentralized feedback gains in both schemes are determined by convex optimization over linear matrix inequalities. We characterize decentralized linear matrix inequality-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with an γ-level ℒ₂-gain. The developed results are tested on a representative example.     

Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state measurement and the second utilizes static output feedback. The decentralized feedback gains in both schemes are determined by convex optimization over LMIs. We characterize decentralized linear matrix inequalities (LMIs)-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with a γ-level ℒ₂-gain. The developed results are tested on a representative example.     

Decentralized stabilization of a class of interconnected systems

Abstract. This paper is concerned with the decentralized stabilization of continuous and discretelinear interconnected systems with the structural constraints about the interconnection matri-ces. For the continuous case,the main improvement in the paper as compared with the corre-sponding results in the literature is to extend the considered class of systems from S to S“ (bothwill be defined in the paper) without resulting in high decentralized gain and difficult numericalcomputation. The algorithm for obtaining decentralized state feedback control to stable theoverall system is presented. The discrete case and some very useful results are discussed aswell.     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.     

具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性

研究了一类具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性.利用时变区间矩阵的分解技术、矩阵的Kronecker积的性质和Lyapunov函数法,得到了该系统均方鲁棒稳定的几个充分性条件.通过一个数值例子说明了所得的这些充分性条件的有效性和实用性.     

具有输入时滞的时滞关联不确定系统的鲁棒分散控制

研究了一类同时具有输入时滞以及不确定参数的时滞关联大系统的稳定性问题.基于所谓的还原法,给出一种新的状态反馈控制器的设计方法,这种方法的不同之处在于利用了时延的大小以及反馈控制的历史信息.根据Lyapunov稳定性理论得到了系统在控制器作用下稳定的充分条件,所有条件都化成可解的标准LMIs(Linear matrix inequalities)形式.文章最后给出了一个数值例子说明本文结果的可行性.     

基于输出反馈的一类大型互联Holder非线性系统的全局实际镇定

本文研究基于输出反馈的一类大型互联Holder连续非线性系统的全局实际镇定问题.通过构造每个子系统的状态观测器,并对观测器的状态作线性变换,得到分散输出反馈控制器.当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.