若干类时滞切换系统的稳定性问题

主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.     

线性连续衰退记忆系统的可分性

为逼近建模和辨识问题的需要,讨论线性时变连续有界输入有界输出稳定衰退记忆系统的不同子类．从衰退记忆系统的子类包括概周期系统,渐近周期系统,渐近强周期系统,找到了LTV系统的可分子空间即渐近强周期系统．     

Sensitivity of non-autonomous discrete dynamical systems

In this paper, the sensitivity for non-autonomous discrete systems is investigated. First of all, two sufficient conditions of sensitivity for general non-autonomous dynamical systems are presented. At the same time, one stronger form of sensitivity, that is, cofinite sensitivity, is introduced for non-autonomous systems. Two sufficient conditions of cofinite sensitivity for general non-autonomous dynamical systems are presented. We generalized the result of sensitivity and strong sensitivity for autonomous discrete systems to general non-autonomous discrete systems, and the conditions in this paper are weaker than the correlated conditions of autonomous discrete systems.     

Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems

In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result, we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints. This research was supported by the National Science Council of the Republic of China.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

A theory for synchronization of dynamical systems

In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense.     

时变离散大系统的稳定性

本文首先给出了线性时变离散系统稳定性的一个充分条件.然后研究当孤立子系统满足上述条件时的线性及非线性时变离散大系统的稳定性.利用向量李雅普诺夫函数法结合时变离散系统的比较原理,得到了时变离散大系统在稳定性中的集结模型.直接由集结系统的稳定性得到大系统稳定性的条件.     

一类混沌系统的函数矩阵投影同步

研究了一类混沌系统的函数矩阵投影同步问题,基于函数矩阵方法,利用Lyapunov稳定性理论和极点配置理论,设计了两个连续混沌系统之间的同步方案,同时设计了两个离散混沌系统之间的同步方案,实现了驱动系统与动态系统按给定的函数矩阵投影同步,并给出了证明,通过对Lorenz混沌系统,和Henon系统的数值模拟,表明了该方法的有效性.     

Some problems of the linear theory of systems of ordinary differential equations

We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet–Lyapunov theory for periodic systems of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula to the introduction of amplitude–phase coordinates in a neighborhood of a periodic trajectory of a dynamical system.     

Lyapunov stability of discontinuous dynamic systems

This paper derives necessary and sufficient conditions for thestability of dynamic systems in the sense of Lyapunov. Theseconditions are used to study the stability of discontinuousdynamic systems, which include fuzzy systems, hybrid systems,and impulsive differentia^! systems.     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

A survey on piecewise-linear models of regulatory dynamical systems

Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems. A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable of demonstrating the essential features of many non-linear dynamical systems is piecewise-linear systems. Implementation of piecewise-linear systems for modelling of regulatory dynamical systems requires different considerations depending on the status of the problem. In this work we considered three different cases. Firstly, we consider the inferential modelling problem based on the empirical observations and study the discrete piecewise-linear system, whose inverse problem is solvable under some assumptions. Secondly, we considered the problem of obtaining some complex regulatory systems by tractable piecewise-linear formulations and study the qualitative dynamic features of the systems and their piecewise-linear models. Finally, we considered Boolean delay equations for building abstract models of regulatory systems, which might be the simplest models demonstrating the essential qualitative features of our interest underlying adaption, learning and memorization.     

Representation of solutions of control hybrid differential-difference impulse systems

We consider linear nonstationary hybrid differential-difference controlled dynamical systems under the action of impulses. For such systems, we derive integral representations of solutions on the basis of the solution of dual (adjoint) systems. This is, in a sense, a generalization to these systems of the Cauchy formula for ordinary systems. This formula is refined in the stationary case. The results are illustrated by an example     

The studies of systems of variational inclusions problems and variational disclusions problems with applications

In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems.     

自治Birkhoff系统的广义正则变换和辛算法研究

研究了自治Birkhoff系统的广义正则变换,将Hamilton系统的辛算法推广到Birkhoff系统,通过引入凯莱变换和生成函数法构造Birkhoff方程的Birkhoff的辛差分格式,同时讨论了Birkhoff差分格式的辛算法.     

Stability and robustness of quasi-linear impulsive hybrid systems

Both hybrid dynamical systems and impulsive dynamical systems are studied extensively in the literature. However, impulsive hybrid systems are not yet well studied. Nonetheless, many physical systems exhibit both system switching and impulsive jump phenomena. This paper investigates stability and robust stability of a class of quasi-linear impulsive hybrid systems by using the methods of Lyapunov functions and Riccati inequalities. Sufficient conditions for stability and robust stability of those systems are established. Some examples are given to illustrate the applicability of our results.     

Transformations of interval linear systems of equations and inequalities

Very recently, new results on transformation of interval linear systems and on generalizations of the Farkas lemma to interval systems appeared in the literature. They are by far not obvious since the standard transformations on linear systems are not easily adapted to interval system due to the dependency problem. The aim of this paper was to come up with new possible transformations and to extend the results to more general classes of AE interval systems and to linear parametric systems. We also show that the transformations can help in simplifying the proofs of some characterization theorems.     

Ten years of genetic fuzzy systems: current framework and new trends

Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. Neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms.The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems. After a brief introduction to models and applications of genetic fuzzy systems, the field is overviewed, new trends are identified, a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated, and open questions that remain to be addressed in the future are raised. The paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems.     

相对论性Birkhoff系统动力学方程的代数结构与Poisson积分方法

定义相对论性Ｐｆａｆｆ作用量,得到相对论性Ｐｆａｆｆ Ｂｉｒｋｈｏｆｆ原理和相对论性Ｂｉｒｋｈｏｆｆ方程．证明了自治形式和半自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程具有相容代数结构和Ｌｉｅ代数结构;一般非 自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程没有代数结构．研究一种特殊的非自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程,它具有相容代数结构和Ｌｉｅ容许代数结构．给出相对论性Ｂｉｒｋｈｏｆｆ方程的Ｐｏｉｓｓｏｎ积分 方法．最后给出应用性实例．     

转动系统相对论性动力学方程的代数结构与Poisson积分

研究转动相对论系统动力学方程的代数结构,得到了完整保守转动相对论系统与特殊非完整转动相对论系统动力学方程具有Lie代数结构;一般完整转动相对论系统、一般非完整转动相对论系统动力学方程具有Lie容许代数结构。并给出转动相对论系统动力学方程的Poisson积分。