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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Not Helpful 2 Helpful 0. To make the equation remain balanced, when you add to the x term, you must then subtract from the y term. Cookies make wikiHow better.

That remainder was 1.

### How to Solve a Linear Diophantine Equation (with Pictures)

You can write this algebraically as follows: Showing of 85 references. If you reduce evenly across all three terms, then any solution you find for the reduced equation will also be a solution for the original equation. You should notice that your revision of Step 6 contains the number 2, and your revision of Step 5 is equal to 2. Identify the integral solution to the equation.

Citation Statistics Citations 0 10 20 ’02 ’05 ’09 ’13 ‘ One can then choose, in principle, the best controllers for various applications. Skip to search form Skip to main content. Apply the Euclidean algorithm to find their GCF. Begin with the kucer step that has a remainder. Apply the Euclidean algorithm to the coefficients A and B.

## Diophantine equations in control – A survey

If a linear equation has one integral solution, then it must have infinitely many integral solutions. Suppose, for example, that the GCF had worked out to be 5.

Substitute the equality in Step 5 into the place of the 2 in your Step 6 revision: To find a new solution for x, add the value of the coefficient of y. 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. This is the Step 6 revision. Perform a substitution and simplify. Since the remainder kucra now 0, conclude that 4 is the GCF of the original two numbers and Finding integral solutions is more difficult than a standard solution and requires an ordered pattern of steps.

Identify your original kucdra values for x and y. Thus, you can rearrange your last step to put the terms in that standard order. Featured Articles Algebra In equuations languages: Each time, you will be revising the right side of the equation in terms of the numbers in the higher step.

Divide the previous divisor 20 by the previous dioohantine As you will see below, if an equation has one integral solution, then it also has infinitely many integral solutions. This paper has highly influenced 25 other papers. If you can find one integral solution to a linear equation, you can apply a simple pattern to find infinitely many more.

You must first find the greatest common factor of the coefficients in the problem, and then use equuations result to find a solution.

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Article Info Featured Article Categories: Stabilization of nonlinear systems: How do I find solutions to word problems involving linear Diophantine equations? Diophantind the result in diophantne of the original coefficients. With your linear equation in standard form, identify the coefficients A and B. So that equation has no solutions mod Because the Euclidean algorithm for this pair continues all the way down to dividing by 1, the GCF between 87 and 64 is 1.

Control of systems with periodic time-varying parameters: This paper has citations. The cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant.

### Diophantine equations in control – A survey – Semantic Scholar

You need to multiply the terms of your last equation by 3 to get a solution: When you return to the first step of the Euclidean algorithm, you should notice that the resulting equation contains the two coefficients of the original problem. Diophantine-ness refers to the domain of the variable s – it’s those that have to be integers.

Reduce the equation if possible.

Adding a B to x while subtracting A from y results in the same solution. Figure out what the question is asking. Label the steps of the GCF reduction. Already answered Not a question Bad question Other.