On “uniformity” in definitions of global asymptotic stability for time-varying nonlinear systems

We discuss the lack of “uniformity” in definitions of uniform global asymptotic stability (UGAS) that have been used in various textbooks, monographs, and papers over the years. Sometimes UGAS is taken to be the combination of uniform local stability (ULS) and uniform global attractivity (UGA). Other times it also encompasses uniform global boundedness (UGB). This paper contains an explicit, smooth scalar example that shows that these definitions do not agree in general, even when the right-hand side is locally Lipschitz in the state uniformly in time (and thus bounded in time). We also discuss various notions of global asymptotic stability with relaxed uniformity (with respect to the initial time) requirements for the behavior of the solutions. In particular, we consider class- estimates and Lyapunov characterizations.     

Robust load-frequency control for uncertain nonlinear power systems: A fuzzy logic approach

A new robust load-frequency control (LFC) methodology is proposed for controlling uncertain nonlinear power systems. Critical nonlinearity in the power system—the valve position limit on the governor, and the parametric uncertainty are concerned. The Takagi-Sugeno fuzzy model of the power system under consideration is first constructed to design the robust fuzzy-model-based LFC. Sufficient conditions for the robust asymptotic convergence of the frequency deviation are then provided in terms of linear matrix inequalities. Boundedness of the other system variables is also studied to ensure justifiable grounds for use of the proposed LFC method. Simulation results convincingly validate the effectiveness of the novel LFC design scheme and the theoretical discussions, which give a positive answer to the quality control of the electric energy.     

收敛自由空间到序列空间lp（1〈p〈∞）无穷矩阵变换集的有界性

研究了从收敛自由空间到序列空间lp（1〈p〈∞）的无穷矩阵变换有界集的特征．给出从一般的收敛自由空间到序列空间lp（1〈p〈∞）的无穷矩阵变换的一般形式,并进一步指出完全收敛自由空间无穷矩阵变换的一般表达式具有简捷的形式．     

基于Petri网分解技术的自动化物流系统建模分析*

针对西安科技大学自动化物流系统的任务规划,提出了一种基于变迁指标和库所指标融合的Petri网分解方法。采用Petri网理论对该物流系统建立模型,给出定义,在此基础上采用提出的Petri网分解方法得到融合了T网和S网特性的最小子网。通过分析该最小子网,得出Petri网模型的活性和有界性,据此推断出物流系统的任务规划合理有效。该方法大大减少了直接分析子网或原Petri网模型的计算量,可避免全局或局部死锁,为系统良好运行提供了依据。     

Non-conservative ultimate bound estimation in LTI perturbed systems

A closed formula for ultimate bound estimation in LTI systems with non-vanishing perturbations is presented. The formula, based on geometrical properties of the system, provides an alternative to Lyapunov's second method based study. Although it is not proven that the bound obtained is always less conservative than the Lyapunov's bound, some examples are introduced where the estimations are significantly improved. An extension of the idea for nonlinear systems is also sketched.     

非线性系统变结构观测器

本文研究了非线性系统的变结构观测器，分别讨论了干扰满足及不满足匹配条件下观测器的鲁棒性，证明了观测器的构造误差是一致最终有界的。     

一类不确定奇异摄动系统的鲁棒控制

本文研究了一类不确定奇异摄动系统，给出了亲折鲁棒控制器的设计方法，仿真结果表明，对这里研究的系统类型，本文所给控制具有更好的抗干扰能力。     

基于分层模糊系统的直接自适应控制

为解决模糊控制器中规则数目随系统变量呈指数增长的问题，利用分层模糊系统设计了一类非线性系统的直接自适应模糊控制器，并证明了所提出的设计方法不但能保证闭环系统的一致有界性。而且可使跟踪误差收敛到原点的小领域内，通过对倒立摆控制的仿真研究验证了该方法的有效性。