Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Stability of discrete systems over a finite interval of time†

In many cases of practical interest there is concern with the behaviour of dynamic systems only over a finite time interval. This concern may arise in one of two ways: In one case the system under consideration is defined over a fixed and finite interval of time, while in the second case the system in question is defined for all time; however, the behaviour of the system is of interest only over a finite time interval.

Recently, Weiss and Infante (1965, 1967) treated the problem of system stability over a finite time interval for the ease of continuous systems. In this paper a theory is developed which concerns itself with the stability of discrete systems over a finite interval of time. The dynamic systems which are considered are general enough so as to include unforced systems, systems under the influence of perturbing forces, linear systems, non-linear systems, time invariant systems, time-varying systems, simple systems and composite systems.

In the present development various definitions of stability are considered and corresponding stability theorems are stated and proved. These theorems yield sufficient conditions for stability and in general involve the existence of Lyapunov-like functions which do not possess the usual definiteness requirements on V and ΔV.     

Evaluation of Fourier transform of impulse response of linear time invariant systems†

Evaluation of the Fourior transform of the system impulse response is an important aspect of the design of control systems. A method suggested hero requires only one cycle of sine or cosine wave to be applied as an input to the system. It is proved that the sum of the sampled values of the output response, at the sampling interval equal to the period of the input wave, directly yields the sign and cosine transforms respectively. The procedure is generalized to any number of complete cycles of input wave, as well as to n/2 cycles whore n is any odd positive integer.     

Construction of regions of stability for non-linear systems containing time delays†

A method has been developed for constructing regions of stability for non-linear systems containing time delays. This method, based on modified Liapunov stability theorems, is applicable to higher-dimensional systems containing several time delays or time-varying delays. A reactor example is presented to illustrate the method.     

A generalized Padé approximation of time delay operator

This paper addresses the problem of fractional order Padé approximation for the time delay operator. Based on optimization method, a fitting polynomial with basic order α is constructed to approximate the time delay operator. This makes for two generalized Padé approximations in the form of normal and symmetric approximation, respectively. The advantage of the proposed method lies in the fact that the resulting approximate model is in the standard transform function form of any commensurate order α, making all of the existing stability analysis methods and control design tools for such systems amenable to the fractional order time delay systems. Some numerical examples are given to demonstrate the effectiveness of the proposed method.     

A nonlinear time series model of El Niño

A smooth transition autoregressive model is estimated for the Southern Oscillation Index, an index commonly used as a measure of El Niño events. Using standard measures there is no indication of nonstationarity in the index. A logistic smooth transition autoregressive model describes the most turbulent periods in the data (these correspond to El Niño events) better than a linear autoregressive model. The estimated nonlinear model passes a battery of diagnostic tests. A generalised impulse response function indicates local instability, but as deterministic extrapolation from the estimated model converges, the nonlinear model may still be useful for forecasting the El Niño Southern Oscillation a few months ahead.     

Acer“Sign of the time”全球记者会专题报道

4月的北京远比预想的要热，近30℃的气温和相对湿度仅10％的干燥空气，让我这个长期生活在“火炉”重庆的人也略感不适。不过，不带一丝阴霾的朗朗清空，也让人的心情格外舒畅。 就在这个阳光灿烂的日子，在咱们的首都北京，我将见证一个对于笔记本电脑界具有里程碑意义的产品系列的诞生。     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

On-line estimation of time delay and continuous-time process parameters†

A simple technique is presented for on-line estimation of constant or slowly-varying continuous-time process parameters and time delay. The method is shown to allow considerable flexibility for application to systems of varying complexity. A major advantage of the algorithm lies in its ability to track time-delay variations over a practically unlimited range. The technique is based on approximation of time delay in the frequency domain by a rational transfer function, construction of the derivatives of process input and output using multiple filters, and estimation using a model which is non-linear in the desired parameters. In spite of this inherent non-linearity with respect to the sought parameters, in general the estimation schemes lead to the true, unique solution. The cases when this is not true are shown not to be of serious consequence.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

How does e-mail use affect perceived control of time?

It is well established in the psychology literature that personality predicts performance to some degree. However, personality neither solely nor directly predicts outcomes. Rather, performance and outcomes unfold through context-specific mediating constructs. This study identified two constructs that mediate the relationship between proactivity and perceived control of time in e-mail use and tested the model with data from 251 knowledge workers. The results show that proactivity predicts the perceived control of time in e-mail use through both e-mail-specific time management behavior and e-mail self-efficacy. Further, greater e-mail self-efficacy leads to improved e-mail-specific time management behavior.     

Population shift bias in tests of space–time interaction

Common to all tests of space–time interaction is the assumption that the population underlying the events of interest exhibits a trajectory of growth that is consistent through time and across space. In practice, however, this assumption is often untenable and, when violated, can introduce population shift bias into the results of these tests. While this problem is widely recognized, more work remains to compare its effect across tests and to determine the extent to which it is a problem for study short periods. This paper quantifies and compares the population shift bias present in the results of the Knox, Mantel, and Jacquez tests of space–time interaction. A simulation study is carried out which quantifies the bias present in each test across a variety of population movement scenarios. Results show a positive relationship between population shift bias and the heterogeneity in population growth across all the tests. They also demonstrate variability in the size of the bias across the three tests for space–time interaction considered. Finally, the results illustrate that population shift bias can be a serious problem for short study periods. Collectively, these findings suggest that an unbiased approach to assessing the significance of space–time interaction test results is needed whenever spatially heterogeneous population change is identified within a study area.     

On the ?2 stability of time varying linear and nonlinear discrete time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.     

An imperfect production process for time varying demand with inflation and time value of money – An EMQ model

The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.     

Assessment of time–frequency representation techniques for thoracic sounds analysis

A step forward in the knowledge about the underlying physiological phenomena of thoracic sounds requires a reliable estimate of their time–frequency behavior that overcomes the disadvantages of the conventional spectrogram. A more detailed time–frequency representation could lead to a better feature extraction for diseases classification and stratification purposes, among others. In this respect, the aim of this study was to look for an omnibus technique to obtain the time–frequency representation (TFR) of thoracic sounds by comparing generic goodness-of-fit criteria in different simulated thoracic sounds scenarios. The performance of ten TFRs for heart, normal tracheal and adventitious lung sounds was assessed using time–frequency patterns obtained by mathematical functions of the thoracic sounds. To find the best TFR performance measures, such as the 2D local (ρ_mean) and global (ρ) central correlation, the normalized root-mean-square error (NRMSE), the cross-correlation coefficient (ρ_IF) and the time–frequency resolution (res_TF) were used. Simulation results pointed out that the Hilbert–Huang spectrum (HHS) had a superior performance as compared with other techniques and then, it can be considered as a reliable TFR for thoracic sounds. Furthermore, the goodness of HHS was assessed using noisy simulated signals. Additionally, HHS was applied to first and second heart sounds taken from a young healthy male subject, to tracheal sound from a middle-age healthy male subject, and to abnormal lung sounds acquired from a male patient with diffuse interstitial pneumonia. It is expected that the results of this research could be used to obtain a better signature of thoracic sounds for pattern recognition purpose, among other tasks.     

Prediction of members’ return visit rates using a time factor

The profit of portal companies in Taiwan is generated by online advertising and e-commerce. Effective advertising requires predicting how users respond to advertisements and then targeting (presenting advertisements) the users in ways that reflect their preferences. The behavioral targeting leverages historical users’ behaviors in order to select for display the ads which are most related to the users’ preferences. Although we may not want to provide advertisements that repeat the same concept, we can exploit predicted return visit rates for the registered members at the specific category of a portal site. However, customers’ preferences change over time. In order to capture the ‘concept drift’, we propose a novel and simple time function to increase/decrease the weight of the old data in evaluating various members’ past behaviors. Then, we construct a member’s Click Preference Index with a Time factor (CPIT) model in order to effectively distinguish the different kinds of member behaviors and predict return visit rates. The marketers of a portal site can thus target the members with high return visit rates and design corresponding marketing strategies. Experimental results with a real dataset have demonstrated that this CPIT model can be practically implemented and provide satisfactory results.     

ℋ∞ stabilisation of switched linear stochastic systems under dwell time constraints

Based on the determination of a minimum dwell time, this article addresses the problem of characterising a switching strategy for ?_∞ stabilisation of switched linear stochastic systems with adapted external inputs. Sufficient conditions that assure exponential mean square stability and an ?_∞ performance index are established by analysing the time evolution of the second-order moment of the state and a recursive dynamic programming inequality, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.     

H∞ control of switched delayed systems with average dwell time

This paper considers the problems of stability analysis and H_∞ controller design of time-delay switched systems with average dwell time. In order to obtain less conservative results than what is seen in the literature, a tighter bound for the state delay term is estimated. Based on the scaled small gain theorem and the model transformation method, an improved exponential stability criterion for time-delay switched systems with average dwell time is formulated in the form of convex matrix inequalities. The aim of the proposed approach is to reduce the minimal average dwell time of the systems, which is made possible by a new Lyapunov–Krasovskii functional combined with the scaled small gain theorem. It is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature. Moreover, the exponential H_∞ controller can be constructed by solving a set of conditions, which is developed on the basis of the exponential stability criterion. Simulation examples illustrate the effectiveness of the proposed method.