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Formulas for Liapunov Functions for Systems of Linear Difference Equations |
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| Authors: | Graef John R; Qian Chuanxi; Zhang Bo |
| Institution: | Department of Mathematics, University of Tennessee at Chattanooga Chattanooga, TN 37403, USA. E-mail: john-graef{at}utc.edu Department of Mathematics and Statistics, Mississippi State University Mississippi State, MS 39762, USA. E-mail: qian{at}math.msstate.edu Department of Mathematics and Computer Science, Fayetteville State University Fayetteville, NC 28301, USA. E-mail: bzhang{at}uncfsu.edu |
| Abstract: | Explicit quadratic Liapunov functions that provide necessaryand sufficient conditions for the asymptotic stability of thesystem of linear difference equations x (t + 1) = Ax(t) areconstructed by transforming the original systems to y (t + 1)= Gy(t), where G is a companion matrix associated with the characteristicpolynomial of A. A necessary and sufficient condition for allroots of the characteristic polynomial to lie in the unit circle|z| < 1 on the complex plane is also derived. 2000 MathematicalsSubject Classification 39A11, 93D05. |
| Keywords: | linear systems of difference equations Liapunov functions asymptotic stability quadratic functions |
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