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Published in:
1986 | OriginalPaper | Chapter
Liapunov’s Direct Method
Author : J. P. LaSalle
Published in: The Stability and Control of Discrete Processes
Publisher: Springer New York
Included in: Professional Book Archive
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In this section, we introduce the concept of Liapunov function in order to discuss stability questions for difference equations. Consider the difference equation 2.1 $${x^1} = Tx,x\left( 0 \right) = {x^0}$$ where as before T: Rm→Rm is continuous. Throughout this section, we assume $$\bar x$$ is an equilibrium solution for (2.1) so $$T\left( {\bar x} \right) = \bar x$$ and $$x\left( n \right) = \bar x$$ is a solution.