Necessary and sufficient conditions for quadratic stabilizability of an uncertain system

Consider an uncertain system (Σ) described by the equationx(t)=A(r(t))x(t)+B(s(t))u(t), wherex(t) ∈R ⁿ is the state,u(t) ∈R ^m is the control,r(t) ∈ ? ?R ^p represents the model parameter uncertainty, ands(t) ∈L ?R ^l represents the input connection parameter uncertainty. The matrix functionsA(·),B(·) are assumed to be continuous and the restraint sets ?,L are assumed to be compact. Within this framework, a notion of quadratic stabilizability is defined. It is important to note that this type of stabilization is robust in the following sense: The Lyapunov function and the control are constructed using only the bounds ?,L. Much of the previous literature has concentrated on a fundamental question: Under what conditions onA(·),B(·), ?,L can quadratic stabilizability be assured? In dealing with this question, previous authors have shown that, if (Σ) satisfies certain matching conditions, then quadratic stabilizability is indeed assured (e.g., Refs. 1–2). Given the fact that matching is only a sufficient condition for quadratic stabilizability, the objective here is to characterize the class of systems for which quadratic stabilizability can be guaranteed.     

H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters

This paper deals with the robust H-control problem for uncertain continuous-time linear time-delay systems with Markovian jumping parameters. Based on Lyapunov functional approach, a sufficient condition that assures the robust stochastic stabilizability and preserves the H-disturbance attenuation for the uncertain class of linear time-delay systems with Markovian jumping parameters is established. The uncertainties considered in this paper are of the norm-bounded type. A numerical example is given to demonstrate the usefulness of the results.     

The principle of robustness in generalized predictive control

This paper deeply analyzes the closed-loop nature of GPC in the framework of internal model control (IMC) theory. A new sort of relation lies in the feedback structure so thatrobust reason can be satisfactorily explained. The result is significant because the previous conclusions are only applied to open-loop stable plant (or model).     

Development and validation of a separation method for the diastereomers and enantiomers of aziridine-type protease inhibitors

Aziridine derivatives are attracting pharmacological interest as protease inhibitors. Due to their two centers of chirality, the aziridines studied here are mixtures of two diastereomers and corresponding enantiomers. Applying cyclodextrin-modified capillary electrophoresis resulted in a baseline separation of the four isomers. The most robust separation was obtained by means of 2 mM sulfated beta-cyclodextrin in 50 mM phosphate buffer of pH 2.5. Using this method, 0.25% of the trans-diastereomers aziridine could be precisely and accurately quantified in the presence of 99.75% of the cis-isomers. The corrected peak-area ratios, migration times, and resolutions were found to be robust with respect to small variations of voltage, buffer concentrations, pH, temperature, chiral selector concentration, and different lots.     

A robust principal component analysis

A robust principal component analysis for samples from a bivariate distribution function is described. The method is based on robust estimators for dispersion in the univariate case along with a certain linearization of the bivariate structure. Besides the continuity of the functional defining the direction of the suitably modified principal axis, we prove consistency of the corresponding sequence of estimators. Asymptotic normality is established under some additional conditions.     

颗粒物质的分形特征与其物理力学性质的关系探讨

从颗粒流的一般本构方程出发,利用室内大型相对密度仪和直接剪切仪,针对粒径分形分布对孔隙率和内摩擦角的影响进行了实验研究。结果表明,在相同实体密度、弹性恢复系数和几何平均中值粒径条件下,随粒径分维数的增大,孔隙率增大,而内摩擦角、颗粒浓度、剪切应力系数与正应力系数均减小。进而分析了粒径分形特性对颗粒流动行为的影响,得出粒径分维数小的颗粒系统剪切应力大,系统的流动性能差,鲁棒性强;反之,分维数大的颗粒系统剪切应力小,系统的流动性能好,敏感性强。对系统组构的分形特征影响系统颗粒物质崩塌流动行为的机制进行了初步探索,为颗粒流系统的研究提供了新思路。     

Geoacoustic inversion based on reflection model of effective density fluid approximation

In order to obtain the physical and geoacoustic properties of marine sediments,an inverse method using reflection loss of different grazing angles is presented.The reflection loss is calculated according to the reflection model of effective density fluid approximation.A two-step hybrid optimization algorithm combining differential evolution and particle swarm optimization along with Bayesian inversion is employed in estimation of porosity,mean grain size,mass density and bulk modulus of grains.Based on the above physical parameters,geoacoustic parameters,including sound speed and attenuation,are further calculated.According to the numerical simulations,we can draw a conclusion that all the parameters can be well estimated with the exception of bulk modulus of grains.In particular,this indirect inverse method for bottom geoacoustic parameters performs high accuracy and strong robustness.The relative errors are 0.092%and 17%,respectively.Finally,measured reflection loss data of sandy sediments at the bottom of a water tank is analyzed,and the estimation value,uncertainty and correlation of each parameter are presented.The availability of this inverse method is verified through comparison between inverse results and part of measured parameters.     

An effective method to improve the robustness of small-world networks under attack

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network.Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario.     

Robustness of Exponential Dichotomies in Infinite-Dimensional Dynamical Systems

In this paper we examine the issue of the robustness, or stability, of an exponential dichotomy, or an exponential trichotomy, in a dynamical system on an Banach space W. These two hyperbolic structures describe long-time dynamical properties of the associated time-varying linearized equation _t +A=B(t) , where the linear operator B(t) is the evaluation of a suitable Fréchet derivative along a given solution in the set K in W. Our main objective is to show, under reasonable conditions, that if B(t)=B(, t) depends continuously on a parameter and there is an exponential dichotomy, or exponential trichotomy, at a value ₀, then there is an exponential dichotomy, or exponential trichotomy, for all near ₀.We present several illustrations indicating the significance of this robustness property.     

Asymptotic Limit of the Bayes Actions Set Derived from a Class of Loss Functions

Similarly to the determination of a prior in Bayesian Decision theory, an arbitrarily precise determination of the loss function is unrealistic. Thus, analogously to global robustness with respect to the prior, one can consider a set of loss functions to describe the imprecise preferences of the decision maker. In this paper, we investigate the asymptotic behavior of the Bayes actions set derived from a class of loss functions. When the collection of additional observations induces a decrease in the range of the Bayes actions, robustness is improved. We give sufficient conditions for the convergence of the Bayes actions set with respect to the Hausdorff metric and we also give the limit set. Finally, we show that these conditions are satisfied when the set of decisions and the set of states of nature are subsets of ^p.