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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Cross out any irrelevant information, then put all the values into your equation.

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Note the new remainder 4. Showing of 85 references. You kucsra first find the greatest common factor of the coefficients in the problem, and then use that result to find a solution. However, that is not the solution to the problem, since the original problem sets 87xy equal to 3.

Divide the previous divisor 20 by the previous remainder If not, then there will be no solution.

Diophantine equations in control – A survey

Not Helpful 0 Helpful 3. If the equation is not already in standard form, you need to use the basic rules of algebra to rearrange or combine the terms to create the standard form.


Help answer questions Learn more. Begin with the last step that has a remainder. Thus, you can rearrange your last step to put the terms in that standard order. Maciejowski Hartmut Logemann Automatica You need to multiply the terms of your last equation by 3 to get a solution: This process will repeat, step by step, until equationz reach the original step of the Euclidean algorithm.

Review the Euclidean algorithm. Thus, you have the following steps: The pattern of infinite solutions begins with the single solution that you identified.

How to Solve a Linear Diophantine Equation (with Pictures)

A linear equation is one that has no exponents greater than 1 on any variables. Topics Discussed in This Paper.

Apply the Euclidean algorithm to the coefficients A and B. To account for the subtraction, you need to change the multiplier 34 to a negative. Subtract the x-coefficient A from the y solution.

Diophantine equations in control – A survey – Semantic Scholar

How do I find solutions to word problems involving linear Diophantine equations? Perform a substitution and simplify. If a linear equation has one integral solution, then it must have infinitely many integral solutions. Both ordinary and diophantine equations can have any type of integer diophanttine non-integer coefficients.

Multiply by the necessary factor to find your solutions. To find a new solution for x, add the value of the coefficient of y. The purpose of this procedure is to wind up with an equation that will be written in terms of 87 and 64, which are the original coefficients of xiophantine problem you are trying to solve.


Citation Statistics Citations 0 dioohantine 20 ’02 ’05 ’09 ’13 ‘ Not Helpful 0 Helpful 0. These are linear equations in a ring and result from a fractional representation of the systems involved. In the original problem, that term is subtracted, but the Euclidean algorithm treats it as a positive term.

As you will see below, if an equation has one integral solution, then it also has infinitely many integral solutions. To find the solution of the linear equation, you will use your work on the Euclidean algorithm as the basis for a repeated process diopahntine renaming and simplifying values. Rewrite the equation in Step 6 as follows: Continuing in this manner, the remaining steps are as follows: Semantic Equattions estimates that this publication has citations based on the available data.