# 10 suggests why these systems cannot be

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Unformatted text preview: re unbounded (Perko, section 1.9, problem 5(d)). Routh-Hurwitz Stability Criteria These criteria determine whether the roots of a polynomial have all negative real parts. When applied to the characteristic polynomial associated with a linear system of equations, they test for asymptotic stability of the equilibrium point. In the 2D case, the characteristic polynomial is . It is easy to see that all of the eigenvalues have negative real parts if and . All of the coefficients of the characteristic polynomial must be positive. In the 3D case, the characteristic polynomial is . All of the eigenvalues have negative real parts if and only if and . See Meiss, problem 2.11. The positivity of the coefficients of the characteristic polynomial is necessary but not sufficient. Analogous stability criteria are available for higher order polynomials. In some cases, it may be much easier to study the stability of a linear system using these criteria than by finding the eigenvalues. 2.8 Nonautonomous Linear Systems and Floquet Theory Let . The initial...
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