John R. Graef, Chuanxi Qian and Bo Zhang

Explicit quadratic Liapunov functions that provide necessary and sufficient conditions for the asymptotic stability of the system of linear difference equations $x (t + 1) = A x(t)$ are constructed by transforming the original systems to $y (t + 1) = G y(t)$, where $G$ is a companion matrix associated with the characteristic polynomial of $A$. A necessary and sufficient condition for all roots of the characteristic polynomial to lie in the unit circle $|z| < 1$ on the complex plane is also derived.

2000 Mathematical Subject Classification: 39A11, 93D05.

Keywords: linear systems of difference equations, Liapunov functions, asymptotic stability, quadratic functions.

E-mail:
john-graef@utc.edu
qian@math.msstate.edu
bzhang@uncfsu.edu