A group of invariant transformations in the stability problem via Lyapunov's first method

Ermolin, Vladislav S.; Vlasova, T. V.

doi:10.1109/icctpea.2014.6893269

“…Using the classic Lyapunov notion of the characteristic number of a function we generalize this concept to matrices and prove the properties of characteristic numbers of matrices and vectors similar to the properties established by Lyapunov for scalar functions. This paper continues the research previously set out in [18,19].…”

supporting

confidence: 76%

“…Let us show that the right-hand side of double inequality (19) holds. The application of the left-hand part of inequality (19) to the matrix X(t) yields the right-hand side of inequality (19). In fact, substituting X −1 for X(t), X(t) for X −1 , and…”

Section: The Relationship Between the Characteristic Number Of A Matrmentioning

confidence: 99%

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Lyapunov’s first method: estimates of characteristic numbers of functional matrices

Ermolin¹,

Vlasova²

2019

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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This paper contains the development of theoretical fundamentals of the first method of Lyapunov. We analyze the relations between characteristic numbers of functional matrices, their rows, and columns. We consider Lyapunov's results obtained to evaluate and calculate characteristic numbers for products of scalar functions and prove a theorem on the generalization of these results to the products of matrices. This theorem states necessary and sufficient conditions for the existence of rigorous estimates for characteristic numbers of matrix products. Also, we prove a theorem that establishes a relationship between the characteristic number of a square non-singular matrix and the characteristic number of its inverse matrix, and the determinant. The stated relations and properties of the characteristic numbers of square matrices we reformulate in terms of the Lyapunov exponents. Examples of matrices illustrate the proved theorems.

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“…First, we consider the problems of stabilization of program motions and kinematic trajectories of dynamic systems. Examples of solving these problems are considered in the works [4][5][6][7][8].…”

Section: Literature Reviewmentioning

confidence: 99%

Use of ERP System to Manage the Economy of Agricultural Complex

Bondarenko*¹,

Zubov²,

Orlov³

et al. 2019

IJITEE

3

0

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The article deals with the issues of the practical application of industrial information system, namely, Enterprise Resource Planning (ERP) in the management of the economy of a diversified agro-industrial complex in the risk farming area. Features of ERP system application are considered taking into account both multidirectional activity of the agricultural enterprise (crop production, animal husbandry, and industrial production), and the complex system of taxation: the presence of a common taxation system and taxation of various activities. Particular attention is paid to the mechanism of closing accounts, and the formation of the actual cost in terms of agricultural production, which is not so much complicated as a laborious and routine task. A huge number of transactions, multiple calculations of the costs distribution bases, the complex structure of the divisions of the very enterprise make the task of automating of process closing period extremely important. The article presents the experience of both the use of ERP system and the training method of specialists in the use of such industrial information systems for automated accounting and management accounting, payroll and personnel accounting, tested at St. Petersburg State University. In consequence of the implementation of the algorithms described in the article, one managed to achieve an increase in both quantitative economic indicators of the agricultural complex, and qualitative indicators, related to the training of specialists in the field of application of ERP systems in agro-industrial complexes

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“…As in [18,19], by χ[X(t)] we denote the characteristic number of a functional matrix X(t). Throughout the paper, we use the following notations: let x j be the j-th column of the matrix X(t); x i be the i-th row of the matrix X(t); let λ j = χ[x j ], λ i = χ[x i ] be the characteristic numbers of the j-th column and of the i-th row of the matrix X(t) correspondingly; let X T (t) be the transposed matrix of X(t); X(t) be the complexconjugate matrix of X(t); X * (t) be the Hermitian conjugate matrix of X(t).…”

mentioning

confidence: 99%

Lyapunov’s first method: estimates of characteristic numbers of functional matrices

Ermolin¹,

Vlasova²

2019

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

Self Cite

0

View full text Add to dashboard Cite

This paper contains the development of theoretical fundamentals of the first method of Lyapunov. We analyze the relations between characteristic numbers of functional matrices, their rows, and columns. We consider Lyapunov's results obtained to evaluate and calculate characteristic numbers for products of scalar functions and prove a theorem on the generalization of these results to the products of matrices. This theorem states necessary and sufficient conditions for the existence of rigorous estimates for characteristic numbers of matrix products. Also, we prove a theorem that establishes a relationship between the characteristic number of a square non-singular matrix and the characteristic number of its inverse matrix, and the determinant. The stated relations and properties of the characteristic numbers of square matrices we reformulate in terms of the Lyapunov exponents. Examples of matrices illustrate the proved theorems.

show abstract

A group of invariant transformations in the stability problem via Lyapunov's first method

Cited by 4 publications

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Lyapunov’s first method: estimates of characteristic numbers of functional matrices

Lyapunov’s first method: estimates of characteristic numbers of functional matrices

Use of ERP System to Manage the Economy of Agricultural Complex

Lyapunov’s first method: estimates of characteristic numbers of functional matrices

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