时变系统的稳定化

This paper deals with the stabilization problem for linear time-varying systems within the framework of nest algebras. We give a necessary and sufficient condition for a class of plants to be stabilizable, and we also study the simultaneous and strong stabilization problems.     

Factorization Systems and Adjunctions

Several results on the translation of factorization systems along adjunctions are proved. The first of these results is the answer to the question posed by G.Janelidze.     

Adjunctions and Locally Transferable Factorization Systems

We present an approach to construct factorization systems in abstract categories. It gives new factorization systems from some given ones, when we have a relevant family of adjunctions between slice categories. The approach is based on the notion of a local factorization system, which is introduced in this paper. Relations between local factorization systems and full replete reflective subcategories of corresponding slice categories are investigated. Several applications of this approach are given.     

时变线性系统的同时稳定性

本文在算子理论框架下研究离散时变线性系统的同时稳定性.给出一个仅依赖于单边强表示的同时稳定性判据和同时镇定控制器的参数化.     

Lur''''e系统稳定与同步的脉冲控制

提出了Lur’e系统的脉冲控制系统，利用关于脉冲系统稳定的几个定理，得到了具变化的脉冲区间的Lur'e系统镇定的充分条件；并且给出了Lur'e系统的适当参数与脉冲控制律，使得两个Lur'e系统脉冲同步。最后，给出数值例子说明本结论的有效性。     

Fundamental groupoids for simplicial objects in Mal'tsev categories

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini).     

Sufficiency-Type Stability and Stabilization Criteria for Linear Time-Invariant Systems with Constant Point Delays

We derive a set of criteria of asymptotic stability for linear and time-invariant systems with multirate point delays. The criteria are concerned with -stability local in the delays and -stability independent of the delays and are classified in several groups according to the technique dealt with. The techniques used include both Lyapunov's matrix inequalities and equalities and Gerschgorin's circle theorem. Lyapunov's inequalities are guaranteed if a set of matrices built from matrices of undelayed and delayed dynamics are stability matrices. Some extensions to robust stability of the above results are also discussed.     

一类二维Markov跳跃非线性时滞系统的镇定控制

研究一类二维Markov跳跃非线性时滞系统的镇定控制问题.给出了Markov跳跃非线性时滞系统解的存在唯一性的一个充分条件,以及系统依概率全局渐近稳定的判别准则.通过构造适当形式的Lyapunov函数,采用积分反推方法给出了一类二维Markov跳跃非线性时滞系统的无记忆状态反馈控制器.证明了在该控制律的作用下,闭环系统平衡点依概率全局渐近稳定.     

棋盘游戏与有限域上多项式分解算法

将有限域F_2上多项式分解问题转化为一种对应的棋盘游戏,利用后者的性质设计了一个F_2上m+n-2次多项式f(x)分解为一个m-1次多项式与一个n-1次多项式的判断、分解算法,并对算法的复杂度进行了分析.算法的一个优势是,如果f(x)不能按要求分解,也可以找到一个与f(x)相近(这里指系数相异项较少)的多项式的分解.     

Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties

El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They also introduced Galois corings as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita context to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.

     

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．     

Sufficiency-Type Stability and Stabilization Criteria for Linear Time-Invariant Systems with Constant Point Delays

A set of criteria of asymptotic stability for linear and time-invariant systems with constant point delays are derived. The criteria are concerned with -stability local in the delays and -stability independent of the delays, namely, stability with all the characteristic roots in Res–<0 for all delays in some defined real intervals including zero and stability with characteristic roots in Res<–<0 as 0⁺ for all possible values of the delays, respectively. The results are classified in several groups according to the technique dealt with. The used techniques include both Lyapunov's matrix inequalities and equalities and Gerschgorin's circle theorem. The Lyapunov's inequalities are guaranteed if a set of matrices, built from the matrices of undelayed and delayed dynamics, are stability matrices. Some extensions to robust stability of the above results are also discussed.     

Optimal State Feedback Input-Output Stabilization of Infinite-Dimensional Discrete Time-Invariant Linear Systems

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a right factorization over H-infinity. A necessary and sufficient condition in terms of an (arbitrary) realization is that each state which can be reached in a finite time from the zero initial state has a finite cost. Another equivalent condition is that the control Riccati equation has a solution (in general unbounded and even non densely defined). The optimal state feedback input-output stabilization problem can then be solved explicitly in terms of the smallest solution of this control Riccati equation. We further show that after renorming the state space in terms of the solution of the control Riccati equation, the closed-loop system is not only input-output stable, but also strongly internally stable. Received: July 4, 2007. Revised: October 17, 2007.     

The Structure and Stabilization Decom position of Linear Interconnected ControlSystem swith Multidelays

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｃｅｏｆＬｙａｐｕｎｏｖｓＲａｎｇｅｏｆｔｈｅＩｎｔｅｒｃｏｎｎｅｃｔｅｄＳｔａｂｉｌｉｚａｔｉｏｎＮｅｗ，ｌｅｔｕｓｃｏｎｓｉｄｅｒｔｈｅｌｉｎｅａｒｃｏｎｓｔａｎｔｉｎｔｅｒｃｏｎｎｅｃｔｅｄｃｏｎｔｒｏｌｓｙｓｔｅｍｘｉ（ｔ）＝∑ｎｊ＝１ａｉｊｘｊ（ｔ）＋∑ｍｊ＝１ｂｉｊｕｊ（ｔ）＋∑Ｎ１ｒ＝１∑ｎｊ＝１ａ（ｒ）１ｉｊｅ（ｒ）１ｉｊｘｊ（ｔ）　　　　　　　　　　＋∑Ｎ２ｓ＝１∑ｎｊ＝１ａ（ｓ）２ｉｊｅ（ｓ）２ｉｊｘｊ（ｔ－ｒ（ｓ）１ｉｊ）＋∑Ｎ２ｄ＝１∑…     

Stability and Stabilization Criteria for a Class of Uncertain Neutral Systems with Time-Varying Delays

In this paper, the robust asymptotic stability and stabilization for a class of uncertain neutral system with time-varying delays are considered. Based on the Lyapunov-Krasovskii functional theory, some stability and stabilization criteria are derived. Delay-dependent and delay-independent criteria are proposed for the stability and stabilization of the considered systems. State and output feedbacks are considered to stabilize the uncertain neutral system. A linear matrix inequality approach and a genetic algorithm are used to solve the stability and stabilization problems. Finally, some numerical examples are shown to illustrate the use of the obtained results.The research reported here was supported by the National Science Council of Taiwan under Grant NSC 91-2213-E-214-016.Communicated by C. T. Leondes     

On Certain Integral Tensor Categories and Integral TQFTs

We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over some ring of algebraic integers. We show how to obtain TQFTs over algebraic integers from these categories.     

Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

In this paper, the problem of the robust stabilization for a class of uncertain linear systems with multiple time-varying delays is investigated. The uncertainty is nonlinear time-varying and does not require a matching condition. A memoryless state-feedback controller for the robust stabilization of the system is proposed. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, two sufficient conditions for the stability are derived. Two numerical examples are given to illustrate the proposed method.     

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.     

多组多滞后区间时变系数线性关联控制系统的结构与关联鲁棒镇定

本文建立了多组多滞后区间时变系数线性关联控制系统的结构概念,采用刘永清建立的鲁棒镇定等价法,给出了具有扰动结构参数的多组多滞后区间时变系数线性关联控制系统的结构与关联鲁棒镇定,同时给出了鲁棒镇定的扰动参数与滞后界限的估计公式。