Feedback stabilization of non-homogeneous bilinear systems with a finite time delay

This paper investigates the feedback stabilization of non-homogeneous delayed bilinear systems, evolving in Hilbert state space. More precisely, under observability like assumption, we prove the exponential and strong stability of the solution by using a bounded feedback control. The partial stabilization is discussed as well. The proof of the main results is based on the decomposition method. The decay estimates of the corresponding solution are obtained. Finally, some examples are presented.

Permanence and Existence of Periodic Solutions for Nicholson’s Blowflies Model with Feedback Control and Delay on Time Scales

Sufficient conditions are established for the permanence in a delayed Nicholson’s blowflies model with feedback control on time scales. Our investigation confirms that the bounded feedback terms do not have any influence on the permanence of this system.