VERYFICATION OF LOCATION PROBLEM IN ECONOMIC RESEARCH

In economic research very often the location problem in the single sample or estimation  of the difference in two samples location is commonly tested by experimental economists. Usually the used tests are Wilcoxon test for single sample location or Wilcoxon – Mann – Whitney for two samples location problem. Unfortunately those tests have some disadvantages such as robustness against assumptions or week efficiency. In the paper, some less known procedures, which allow avoid those problems, will be presented. Considered methods will be illustrated on the example of the data  analysis from real-estate market

Bounded real lemmas for positive descriptor systems

A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results

The Methodology of Carrying Out Empirical Research on the Cumulative Effect of the Factors Generating Construction Delays

AbstractThe aim of this article is to present the model of carrying on empirical research of the cumulative effect of the factors generating delays on the construction site. The paper describes the successive stages of the proceedings, the process of implementing the model, the problems that emerged during the research and the directions for further research work. Moreover, it was developed graphical model structure decision, which shows the successive stages of research

The Use of Combined Multicriteria Method for the Valuation of Real Estate

A considered problem is a valuation of real estate. It is important to specify their exact market value, which is the result of several factors. Valuation of property is made on the basis of information and transactions on the local market. Moreover, the valuation always is based on the data of the similar properties. A comprehensive set of data is needed for these reasons. It is quite confusing because the number of transactions on the local market often is not sufficient. The purpose of this paper is to present a method for multicriteria valuation of real estate. This procedure is based on the Analytic Hierarchy Process (AHP) and the Goal Programming (GP). It was designed especially for valuation in situation in which information are limited. The proposed method was used for the valuation of the real estate located on [email protected] of Economic Sciences, Warsaw University of Life Sciences5(71)20821

A direct method to obtain a realization of a polynomial matrix and its applications

[EN] In this paper we present a Silverman-Ho algorithm-based method to obtain a realization of a polynomial matrix. This method provides the final formulation of a minimal realization directly from a full rank factorization of a specific given matrix. Also, some classical problems in control theory such as model reduction in singular systems or the positive realization problem in standard systems are solved with this method.Work supported by the Spanish DGI grant MTM2017-85669-P-AR.Cantó Colomina, R.; Moll López, SE.; Ricarte Benedito, B.; Urbano Salvador, AM. (2020). A direct method to obtain a realization of a polynomial matrix and its applications. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-15. https://doi.org/10.1007/s13398-020-00819-1S1151142Anderson, B.D.O., Bongpanitlerd, S.: Network Analysis and Synthesis, A Modern Systems Theory Approach. Prentice-Hall Inc., New Jersey (1968)Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Trans. Autom. Control 49(5), 651–664 (2004). https://doi.org/10.1109/TAC.2004.826715Bru, R., Coll, C., Sánchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl. 349, 1–10 (2002). https://doi.org/10.1016/S0024-3795(02)00277-XCantó, R., Ricarte, B., Urbano, A.M.: Positive realizations of transfer matrices with real poles. IEEE Trans. Circuits Syst. II Expr. Br. 54(6), 517–521 (2007). https://doi.org/10.1109/TCSII.2007.894408Cantó, R., Ricarte, B., Urbano, A.M.: On positivity of discrete-time singular systems and the realization problem. Lect. Notes Control Inf. Sci. 389, 251–258 (2009). https://doi.org/10.1007/978-3-642-02894-6_24Climent, J., Napp, D., Requena, V.: Block Toeplitz matrices for burst-correcting convolutional codes. RACSAM 114, 38 (2020). https://doi.org/10.1007/s13398-019-00744-yDai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, New York (1989)Golub, G.H., Van Loan, C.F.: Matrix Computations, Fourth edn. Johns Hopkins University Press, Baltimore (2013)Henrion, D., Šebek, M.: Polynomial and matrix fraction description. In: Control Systems, Robotics and Automation, vol. 7, pp. 211-231, (2009). http://www.eolss.net/Sample-Chapters/C18/E6-43-13-05.pdfHo, B.L., Kalman, R.E.: Effective construction of linear state-variable models from mput/output functions. Regelungstechnik 14(12), 545–548 (1966)Kaczorek, T.: Weakly positive continuous-time linear systems. Lect. Notes Control Inf. Sci. 243, 3–16 (1999)Kaczorek, T.: Positive 1D and 2D Systems, vol. 431. Springer, London (2002)Kaczorek, T.: Externally and internally positive singular discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 12(2), 197–202 (2002)MATLAB, The Math Works, Inc., Natick, Massachusetts, United States. Official website: http://www.mathworks.comMcCrory, C., Parusinski, A.: The weight filtration for real algebraic varieties II: classical homology. RACSAM 108, 63–94 (2014). https://doi.org/10.1007/s13398-012-0098-ySilverman, L.: Realization of linear dynamical systems. IEEE Trans. Autom. Control 16(6), 554–567 (1971)Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429(10), 2640–2659 (2008

Distributed Control of Positive Systems

A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage functions can be used instead of quadratic ones. This paper shows how such methods can be used for synthesis of distributed controllers. It also shows that stability and performance of such control systems can be verified with a complexity that scales linearly with the number of interconnections. Several results regarding scalable synthesis and verfication are derived, including a new stronger version of the Kalman-Yakubovich-Popov lemma for positive systems. Some main results are stated for frequency domain models using the notion of positively dominated system. The analysis is illustrated with applications to transportation networks, vehicle formations and power systems

Positive Descriptor Time-varying Discrete-time Linear Systems and Their Asymptotic Stability

The positivity and asymptotic stability of the descriptor time-varying discrete-time linear systems are addressed. The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to the time-varying discrete-time descriptor linear systems. Using the extension necessary and sufficient conditions for the positivity of the systems are established. Sufficient conditions for asymptotic stability of the positive systems are presented. The effectiveness of the tests is demonstrated on the example

Some recent developments in theory of fractional positive and cone linear systems

The overview of some recent developments and new results in the theory of fractional positive and cone one-dimensional (1D) and two-dimensional (2D) linear systems are presented in the article. The state equations and their solution for the fractional continuous-time and discrete-time linear systems are given. Necessary and sufficient conditions for the internal and external positivity of the fractional linear systems are established. The reachability of the fractional linear systems is addressed. A new notation of the cone systems is introduced and methods for computation of such systems are proposed. Positive fractional 2D linear systems are intoduced. Necessary and sufficient conditions for the positivity and reachability are established. The considerations are illustrated with many examples of 1D and 2D linear systems.Запропоновано огляд та деякі нові результати у теорії фракційних додатніх та конусних одновимірних (1D) та двовимірних (2D) лінійних систем. Подано рівняння стану та їхнє розв’язання для фракційних неперервних та дискретних лінійних систем. Встановлено необхідні та достатні умови для внутрішньої та зовнішньої додатності фракційних лінійних систем. Показано їхню досяжність. Запропоновано нову форму запису конусних систем та методи, придатні для комп’ютерного розрахунку таких систем. Представлено додатні фракційні 2D лінійні системи. Встановлено необхідні та достатні умови для додатності та досяжності. Теоретичні виклади проілюстровано чисельними прикладами 1D та 2D лінійних систем.Предложены анализ состояния вопроса и некоторые новые результаты, полученные в теории фракционных положительных и конусных одномерных (1D) и двумерных (2D) линейных систем. Приведены уравнения состояния и их решения для фракционных непрерывных и дискретных линейных систем. Выявлены необходимые и достаточные условия для внутренней и внешней положительности фракционных линейных систем. Показана их достижимость. Предложена новая форма записи конусных систем, а также методы их компьютерного расчета. Представлены положительные фракционные 2D линейные системы. Установлены необходимые и достаточные условия для положительности и достижимости. Теоретические выкладки иллюстрированы численными примерами 1D и 1D линейных систем