On the Robustness of Positive Linear Systems in Infinite Dimension
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Date
2025
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Abstract
In the present research, it has been demonstrated that an explicit robust stability
bound is generalized from the finite dimensional case to the infinite dimensional
case. The systems that were investigated are known as Positive Linear Time-Delay
Differential Systems (PLTDDS (s)), and they are subject to time-varying structural
perturbations in Banach lattices. The Semigroup Method, the Principle of
Comparison, and the Perron-Frobenius Theorem are all utilized in the current
study. Furthermore, the coincidence of complex, real, and positive stability radii
for a variety of particular cases is also demonstrated, and an explicit formula for
the radius is derived. This is in addition to the radius that is described in detail.