Sufficient and necessary conditions for uniform exponential stabilisation of abstract infinite-dimensional bilinear systems with distributed delay

In this paper, we address the problem of uniform exponential stabilisation for a class of abstract infinite-dimensional bilinear systems with distributed delay. Furthermore, we establish uniform exponential stabilisation result under a new sufficient and necessary condition and provide an explicit decay rate estimate for the stabilised state system. Partial strong stabilisation is also discussed. Various applications, including numerical simulations, are considered.