An LMI condition for asymptotic stability of discrete-time system based on quadratic difference forms

This paper is concerned with the stability analysis of a linear discrete-time system described by a high-order difference-algebraic equation. It is well known that, in the behavioral approach, a Lyapunov for a linear system is characterized in terms of a so-called quadratic difference form (QDF). For a discrete-time case, Kojima and Takaba (2005) derived a necessary and sufficient condition for the asymptotic stability in terms of the QDFs. On the basis of this QDF condition, we derive a numerically more tractable stability condition in terms of LMIs.