Unformatted text preview: re unbounded (Perko, section 1.9, problem 5(d)). RouthHurwitz 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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 Fall '14
 MarcEvans
 Linear Algebra, Complex number, Floquet Theory

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