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Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 35--56 | DOI:10.5890/DNC.2023.03.004

Leila Yahiaoui, Maissa Kada, Abdelaziz Mennouni

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Abstract

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

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