Binary trees with choosable edge lengths

For a set of two-element sets of non-negative real numbers we consider rooted strict binary trees with the property that the two edges leading from every non-leaf to its two children are assigned lengths l₁ and l₂ with {l₁,l₂}∈L.For choices of L for which l₁+l₂ is constant for every {l₁,l₂}∈L which models that a certain total length can be distributed with some degree of freedom specified by L to incident edges, we study the asymptotic growth of the maximum number of leaves of bounded depths in such trees and the existence of such trees with leaves at individually specified maximum depths.     

一类执行器幅值与速率受限的线性系统静态抗饱和综合

讨论一类线性约束系统的静态抗饱和综合问题, 将执行器动力学特性引入增广系统, 从而化原系统为仅有幅值饱和的高阶增广系统. 提出基于线性矩阵不等式(LMI)的优化算法, 求得的静态抗饱和增益同时保证闭环系统的局部稳定性与最小化的L2增益. 仿真算例验证了方法的有效性.     

具有区间时滞的不确定性随机时滞系统的时滞相关鲁棒稳定性

针对具有区间时滞的不确定性随机时滞系统, 进行稳定性分析. 通过考虑变时滞、时滞的上界及它们的差三者之间的关系, 并应用公式和Lyapunov稳定性理论, 在不忽略任何有用项的前提下, 得到改进的具有区间时滞的随机系统的稳定性判据. 数值实例验证了该方法的有效性.     

A less conservative robust stability criteria for uncertain neutral systems with mixed delays

This paper is concerned with the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. By considering the cross-terms with additional design parameters, a complete form of Lyapunov–Krasovskii functional is constructed. Then some free weighting matrices are introduced, and a sufficient stability condition is obtained in terms of linear matrix inequalities. The obtained criterion is dependent on the sizes of neutral delay and discrete delay and are less conservative than those produced by previous approaches. Numerical examples are given to illustrate both the improvement the proposed method provides over some existing ones and the relationship between the neutral- and discrete-delay.     

Interconnection-based performance analysis for a class of decentralized controllers

This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and scalar optimization problems will both be equal to zero.     

New absolute stability criteria for time‐delay Lur'e systems with sector‐bounded nonlinearity

This paper is concerned with the problem of absolute stability of time‐delay Lur'e systems with sector‐bounded nonlinearity. Several novel criteria are presented by using a Lur'e–Postnikov function. For a general Lur'e system with known time delay, the absolute stability of it is analyzed by solving a set of linear matrix inequalities (LMIs). The maximum upper bound of the allowable time delay for a general Lur'e system is derived by solving a convex optimization problem. The feasibility of the LMIs implies some frequency‐domain interpretations which are similar to the frequency‐domain inequalities in the circle criterion and the Popov criterion. Copyright © 2009 John Wiley & Sons, Ltd.     

New delay‐dependent stability analysis and synthesis of T–S fuzzy systems with time‐varying delay

In this paper, a new method is proposed for stability analysis and synthesis of Takagi–Sugeno (T–S) fuzzy systems with time‐varying delay. Based on a new Lyapunov–Krasovskii functional (LKF), some less conservative delay‐dependent stability criteria are established. In the derivation process, some additional useful terms, ignored in previous methods, are considered and new free‐weighting matrices are introduced to estimate the upper bound of the derivative of LKF for T–S fuzzy systems with time‐varying delay. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

具有状态观测器的鲁棒重复控制系统设计

针对一类时变不确定系统,研究基于状态观测器的鲁棒重复控制系统设计问题.通过状态观测器重构系统状态,利用重构状态进行状态反馈.基丁2维系统稳定性理论,应川线性矩阵不等式(LMI)方法,推导出了重复控制系统存在状态观测器和重复控制器的一个LMI条件,并用LMI的町行解给出了状态观测器和重复控制器参数的具体形式.最后用数值仿真验证了本文所提方法的有效性.     

基于LMI的分布时滞系统输出动态反馈镇定

研究分布时滞系统的输出动态反馈镇定问题. 基于闭环系统的中立型变换及相应Lyapunov-Krasovskii泛函的构造与解析技巧, 建立了与时滞相关的控制器存在性判据. 在此基础上通过控制器参数化设计方法, 将控制器参数的求解归结为线性矩阵不等式解的形式. 仿真算例验证了方法的有效性