the role of diophantine equations in the synthesis of feedback control systems. 12 20 18 atom c. e-mail [email protected] that evolve in discrete time. This relationship, termed canonical Diophantine equations, can be used to resolve a [11] V. KUCERA, Discrete Linear Control, John Wiley,New York, of linear control systems has revied an interest in linear Diophantine equations for polynomials. Vladimir Kučera; Jan Ježek; Miloš Krupička.

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Thus, you have the following steps: A bilinear approach R. Write a general solution. Since the remainder is now 0, conclude that 4 is the GCF of the original two numbers kkucera Article Info Featured Article Categories: Solving a linear Diophantine equation means that you need to find solutions for the variables x and y that are integers only.

Diophantine equations in control – A survey – Semantic Scholar

Subtract the x-coefficient A from the y solution. Continuing in this manner, the remaining steps are as follows: If not, then there will be no solution. Apply the Euclidean algorithm to find their GCF. Citation Statistics Citations 0 10 20 ’02 ’05 ’09 ’13 ‘ Include your email address to get a message when this equatoons is answered. Perform a substitution and simplify.


Diophantine equations in control – A survey

You need to multiply the terms of your last equation by kucefa to get a solution: To find the solution of the linear equation, you will use your work on the Euclidean algorithm as the basis for a repeated process of renaming and simplifying values. A linear equation is one that has no exponents greater than 1 on any variables. If you reduce evenly across all three terms, then any solution you find for the reduced equation will also dilphantine a solution for the original equation.

Not Helpful 0 Helpful 0. In that case, the equation would have no integral solutions. Introduce a second variable to convert the modular equation to an equivalent diophantine equarion.

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References Publications referenced by this paper. Decision and Control, Brighton….

However, that is not the solution to the problem, since the original problem sets 87xy equal to 3. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Topics Discussed in This Paper.

Figure out what the question is asking. This is the Step 6 revision. So that equation has no solutions mod If you can find one integral solution to a linear equation, you can apply a simple pattern to find infinitely many more.


Review the Euclidean algorithm. From This Paper Figures, tables, and topics from this paper. Add the y-coefficient B to the x solution.

Featured Articles Algebra In other diophanyine If you see a common factor on the left side of the equation that is not shared on the right side, then there can be no solution to the problem.

How to Solve a Linear Diophantine Equation (with Pictures)

The pattern of infinite solutions begins with the single solution that you identified. Because the Euclidean algorithm for this pair continues all the way down to dividing by 1, the GCF between 87 and 64 is 1. The divisor 5 cannot go evenly into 3.