Abstract
This paper presents two significant contributions: First, we examine linear infinite-dimensional systems perturbed in deterministic and stochastic ways. The stability radius method is used to solve the robust stability. Bounds on the perturbations are obtained, guaranteeing that the troubled system is stable. The outcomes are determined via a Lyapunov equation. Secondly, we study the robust stabilisation problem. We investigate the maximisation of the stability radius when the input operator is unbounded in the general case. Also, we establish the conditions under which suboptimal controllers exist. An infinite-dimensional Riccati equation describes the supreme achievable stability radius.
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