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A Generalized Lyapunov Stability Theorem for Discrete-time Systems based on Quadratic Difference Forms

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2 Author(s)
C. Kojima ; Department of Applied Mathematics and Physics, Kyoto University, Yoshida-Honmachi, Sakyo-Ku, Kyoto, 606-8501, Japan. ; K. Takaba

In this paper, we consider the generalized Lyapunov stability analysis for a discrete-time system described by a high order difference-algebraic equation. In the behavioral approach, a Lyapunov function is characterized in terms of a quadratic difference form. As a main result, we derive a generalized Lyapunov stability theorem that the asymptotic stability of a behavior is equivalent to the solvability of the two-variable polynomial Lyapunov equation (TVPLE) whose solution induces the Lyapunov function. Moreover, we derive another asymptotic stability condition by using a polynomial matrix solution of the one-variable dipolynomial Lyapunov equation which is reduced from the TVPLE.

Published in:

Proceedings of the 44th IEEE Conference on Decision and Control

Date of Conference:

12-15 Dec. 2005