Formulas for Liapunov functions for systems of linear difference equations

• Autores: Chuanxi Qian, John R. Graef, Bo Zhang
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 88, Nº 1, 2004, págs. 185-203
• Idioma: inglés
• DOI: 10.1112/s0024611503014308
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• Resumen

  • 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.