Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.

In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when the Nyquist frequency is larger or equal to the maximal frequency in the spectrum of a signal sampled. We demonstrate that this seemingly obvious observation has wideranging implications. They are discussed here in detail. Furthermore, we discuss also signal shaping effects that occur in the case of signal under-sampling. That is, when the Nyquist frequency is smaller than the maximal frequency in the spectrum of a signal sampled. Further, we explain the mechanism of a specific signal distortion that arises under these circumstances. We call it the signal shaping, not the signal aliasing, because of many reasons discussed throughout this paper. Mainly however because of the fact that the operation behind it, called also the signal shaping here, is not a filtering in a usual sense. And, it is shown that this kind of shaping depends upon the sampling phase. Furthermore, formulated in other words, this operation can be viewed as a one which shapes the signal and performs the low-pass filtering of it at the same time. Also, an interesting relation connecting the Fourier transform of a signal filtered with the use of an ideal low-pass filter having the cut frequency lying in the region of under-sampling with the Fourier transforms of its two under-sampled versions is derived. This relation is presented in the time domain, too.

The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.

The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.

In the ironmaking, sizes of raw materials such as iron ores and coke must be adjusted for subsequent process in the blast furnace. The depletion of high grade iron ore in recent years necessitates a technology that can utilize low-grade fine iron ores. Thus, steelmakers have been studying the sinter-briquette complex firing process that employs a method of charging the sinter feed together with briquettes made of fine iron ore. In this process, larger briquettes increase the briquette productivity per unit time but decrease the green strength of briquettes and they can break during transportation and charging. Thus, the briquette shape is very important.

Therefore, in this study, we simulate a twin roll briquetting process using the DEM analysis and compared the compressive force distributions in the briquette for different aspect ratios. This study is a new attempt, because research cases by numerical methods on the same or similar systems are very rare. Consequently, the optimal aspect ratio is 0.5 at briquette height 20 mm, 2.0 at 30 mm, and 1.5 at 40 mm. Also, the average compressive force increased in proportion with the pocket height at the same aspect ratio. Therefore, to increase the pocket depth for high productivity, the pocket height must also be increased for obtaining high strength briquettes.

The article introduces an innovative approch for the inspection challenge that represents a generalization of the classical Traveling Salesman Problem. Its priciple idea is to visit continuous areas (circles) in a way, that minimizes travelled distance. In practice, the problem can be defined as an issue of scheduling unmanned aerial vehicle which has discrete-continuous nature. In order to solve this problem the use of local search algorithms is proposed.

With the rapid advancement of digital processors, filters have been commonly implemented using microcomputers. In this study, a low-cost and compact Arduino Uno development board was used to realize digital lead and lag compensators. Arduino boards are very affordable. Consequently, they were investigated to see if they were capable of preserving the frequency response of continuous-time compensators. The experiments required a set of equipment including a function generator, an Arduino Uno development board, a PC-based oscilloscope, and a laptop. The signal frequency was varied from 0 to 500 Hz. Two discretization methods were employed, namely bilinear transformation and matched pole-zero mapping. The results showed that an Arduino Uno board can be utilized to implement lead and lag compensators to some extent. The discrete-time compensator preserved the capability of filtering out certain frequencies. The change in DC gain was negligible, however, there was a significant difference in the cut-off frequency and transient slope. For both discretization methods, the frequency responses at high frequency experienced a rippling profile.

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

The paper considers developed and offered an effective algorithm for solving the block-symmetrical tasks of polynomial computational complexity of data processing modular block-schemes designing. Currently, there are a large number of technologies and tools that allow you to create information systems of any class and purpose. To solve the problems of designing effective information systems, various models and methods are used, in particular, mathematical discrete programming methods. At the same time, it is known that such tasks have exponential computational complexity and can not always be used to solve practical problems. In this regard, there is a need to develop models and methods of the new class, which provide the solution of applied problems of discrete programming, aimed at solving problems of large dimensions. The work has developed and proposed block-symmetric models and methods as a new class of discrete programming problems that allow us to set and solve applied problems from various spheres of human activity. The issues of using the developed models are considered. and methods for computer-aided design of information systems (IS).

The problem of performing software tests using Testing-as-a-Service cloud environment is considered and formulated as an~online cluster scheduling on parallel machines with total flowtime criterion. A mathematical model is proposed. Several properties of the problem, including solution feasibility and connection to the classic scheduling on parallel machines are discussed. A family of algorithms based on a new priority rule called the Smallest Remaining Load (SRL) is proposed. We prove that algorithms from that family are not competitive relative to each other. Computer experiment using real-life data indicated that the SRL algorithm using the longest job sub-strategy is the best in performance. This algorithm is then compared with the Simulated Annealing metaheuristic. Results indicate that the metaheuristic rarely outperforms the SRL algorithm, obtaining worse results most of the time, which is counter-intuitive for a metaheuristic. Finally, we test the accuracy of prediction of processing times of jobs. The results indicate high (91.4%) accuracy for predicting processing times of test cases and even higher (98.7%) for prediction of remaining load of test suites. Results also show that schedules obtained through prediction are stable (coefficient of variation is 0.2‒3.7%) and do not affect most of the algorithms (around 1% difference in flowtime), proving the considered problem is semi-clairvoyant. For the Largest Remaining Load rule, the predicted values tend to perform better than the actual values. The use of predicted values affects the SRL algorithm the most (up to 15% flowtime increase), but it still outperforms other algorithms.

Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems are established. It is shown that if the fractional system is pointwise complete in one step (q = 1), then it is also pointwise complete for q = 2, 3…