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Show that asymptotic stability of the adaptation error is assured for $0<\gamma<2, \alpha>0$.

$$ \hat{\theta}(t + 1) = \hat{\theta}(t) + \frac{\gamma \phi(t)\varepsilon^{0}(t + 1)}{\alpha + \phi^T(t)\phi(t)} $$

Any ideas? Would someone give me some references link?

Thank you.

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  • $\begingroup$ Can you please provide more context? $\endgroup$ – EDZ Feb 19 '18 at 0:04
  • $\begingroup$ What is $\varphi$, $\varepsilon$? $\endgroup$ – Carlos Feb 19 '18 at 7:02
  • $\begingroup$ This is about parameter adaptation algorithm an improved gradient algoritm $\endgroup$ – user3483851 Feb 22 '18 at 23:02

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