Riesz-Thorin Theorem and $l_p$-Stability of Nonlinear Time-Varying Discrete Systems

Venkatesh, YV (1988) Riesz-Thorin Theorem and $l_p$-Stability of Nonlinear Time-Varying Discrete Systems. In: Journal of Mathematical Analysis and Applications, 135 (2). pp. 627-643.

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Abstract

The interpolation theorem due to Riesz-Thorin is used along with Hölder's and Young's inequalities to derive some new conditions, more general than those in the literature, for the $I_p$-stability $(1 \leq, p \leq \infty)$ of a class of nonlinear time-varying discrete systems represented by a time invariant linear discrete part G in feedback with a discrete nonlinear time-varying gain $k(n) \varphi (\cdot)$. These stability conditions are expressed in terms of a general multiplier (causal + anticausal) function and global upper and lower bounds on the normalized rate of growth, (k(n + 1)/k(n)), of the time-varying gain.

Item Type: Journal Article Copyright for this article belongs Elsevier. Riesz-Thorin;theorem;stability;nonlinear;time-varying;discrete systems. Division of Electrical Sciences > Electrical Engineering 18 Aug 2008 19 Sep 2010 04:49 http://eprints.iisc.ernet.in/id/eprint/15565