Feedback stabilisation and polynomial decay estimate for distributed bilinear parabolic systems with time delay

In this paper, we examine the feedback stabilisation for distributed bilinear parabolic systems described by partial differential equation with time delay. The stabilisation of a such system reduces stabilising only its projection on a suitable subspace. To this end, we will propose a continuous feedback control that guarantees the strong stabilisation under a weaker observability assumption. An explicit decay rate estimate of the stabilised state is also given. Besides, some illustrating examples and simulations are provided.