Erschienen in:

1986 | OriginalPaper | Buchkapitel

Liapunov’s Direct Method

verfasst von : J. P. LaSalle

Erschienen in: The Stability and Control of Discrete Processes

Verlag: Springer New York

Enthalten 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.

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