# Combine two different size matrix in state equations

• khedira
In summary, The conversation discusses two sets of state equations with different sizes for A, B, and C. The individual equations are given, and the question is raised about adding A from the two sets together. After some confusion and consideration, it is determined that the addition is possible by using the identity matrix.
khedira
i have two sets of state equations:

1) x(dot) = (2x2)x + (2x1)u
y = (1x2)x

2) x(dot) = (0)x + (1x1)u
y = (1x1)x

given the above, since A, B and C are of different sizes, how can i add the A from 1) and 2) to get a combined A? Is that possible? Please advise. Thank you.

what are A, B & C? can you explain better?

also what are x,y & u are these 2x1 column vectors etc.

lanedance said:
what are A, B & C? can you explain better?

also what are x,y & u are these 2x1 column vectors etc.

Hi lanedance,

The problem was that i have this A1 2x2 matrix, e.g. [1 2; 3 4] and i have another A2 1x1 matrix [5]. I wish to add them together, i.e. A = A1 + A2. At first i thought that the size different between A1 and A2 make it impossible to directly add them up. Then i realize that since A2 is in scalar form, A = A1 + A2 = [6 7; 8 9].

yeah that doesn't seem quite right, maybe if its A2*I , where I is the identity matrix it works

## 1. How do you combine two different size matrices in state equations?

The most common way to combine two different size matrices in state equations is by using the Kronecker product. This involves multiplying the first matrix with the identity matrix of the same size as the second matrix, and then multiplying the second matrix with the identity matrix of the same size as the first matrix. The results of these two operations are then added together to create the combined matrix.

## 2. Can you use other methods to combine two different size matrices in state equations?

Yes, there are other methods that can be used to combine two different size matrices in state equations, such as block matrix multiplication or padding one matrix with zeros to make it the same size as the other matrix. However, the Kronecker product is often the most efficient and widely used method.

## 3. What is the purpose of combining two different size matrices in state equations?

Combining two different size matrices in state equations is necessary when representing a system with multiple inputs and outputs. It allows for a more compact and efficient representation of the system, making it easier to analyze and solve.

## 4. Are there any limitations to combining two different size matrices in state equations?

One limitation is that the resulting combined matrix may become very large and complex, making it difficult to interpret and solve. In some cases, the combined matrix may also become ill-conditioned, which can affect the accuracy of the results.

## 5. Are there any special considerations when combining two different size matrices in state equations?

Yes, it is important to ensure that the matrices being combined are compatible and represent the same system. This means that the dimensions and order of the matrices must be carefully considered. It is also important to understand the properties of the Kronecker product and how it affects the resulting combined matrix.

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