Hi,

Using these definitions:

A homogeneous equation with constant coefficients is said to be stable if all solutions remain bounded as t-->infinity

A homogeneous equation with constant coefficients is said to be asymptotically stable if all solutions converge to the zero solution as t-->infinity

I'm trying to prove these two statements:

1) The system is stable if and only if for every root of the characteristic polynomial, and if the multiplicity of lambda is bigger than one.

2) The system is aymptotically stable if and only if for every root of the characteristic polynomial, .

Thanks a lot!