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For each of the following systems find a bound on a such


Problem 1. For each of the following systems, find a bound on |a| such that the origin is exponentially stable.

(1) x·1 = - x1 - 2x2 + a(x1 - x2)||x||2,  x·2 = 2x1 - x2 - a(x1 + x2)||x||2

(2) x·1 = ax12 + x2,  x·2 = -x1 - x13/(1 + x12) - x2

(3) x·1 = x2, x·2 = - x1 - x2 + a (x1 - x2)

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Engineering Mathematics: For each of the following systems find a bound on a such
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