This problem came up in a project I'm doing for work, and I don't have a very extensive math background so I don't know how to solve it. I would appreciate any help you guys could give me.(adsbygoogle = window.adsbygoogle || []).push({});

X_{1}is a constant

Y_{1}is a constant

X_{n}= aX_{n-1}+ bY_{n-1}

Y_{n}= cX_{n-1}+ dY_{n-1}

For all n, for some constants a,b,c,d (for my purposes, all between -1 and 0).

What is the sum X_{1}+ X_{2}+ ... to infinity?

I've tried summing it like an infinite series:

(1/(1-a))(x+b((1/(1-d)y + cx))

That gives me a (poor) approximation, but not the exact answer :-(.

Thank you so much for your help in advance!

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# Autonomous System Summation

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