Stability of a Matrix

Suppose I have an n x n matrix A [ 0 1 0 ... 0 ] [ 0 0 1 ... 0 ] [ 0 0 0 ... 0 ] [ ... ... ... ... ... ]
[ 0 0 0 0 1 ] [ x_1 x_2 x_3 ... x_n ]
i.e., a companion matrix where each of the elements of the last row is
x_i = [1 - 1 / (1 + r)] a_i a_i = any real number
for i = 1 ... n
If r = 0, then x_i = 0 for all i and the matrix has all eigenvalues at the origin.
My question is, what is the range of r such that every eigenvalue of the matrix is within the unit circle?
Thanks.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.