Find a bound on a such that the origin

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Reference no: EM131204589

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)

Reference no: EM131204589

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