Discontinuity, Nonlinearity, and Complexity
Stability Radii of InfiniteDimensional DiscreteTime Systems Discomfited by Stochastic Perturbations
Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 3556  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 infinitedimensional linear discretetime 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 infinitedimensional discretetime Riccati equation. Examples are provided to demonstrate the achieved outcomes.
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