On controller design for delay-independent stability of linear time-invariant systems with multiple delays

In this paper, we present a new control-design procedure for linear time-invariant (LTI) systems with “multiple” delays. These procedures are based on algebraic tools and allow designing controllers that can stabilize such systems regardless of how large/small the delays are. That is, with these controllers, the system at hand can be rendered delay-independent stable (DIS). The essence of the control design is based on the Rekasius transformation, algebraic tools, elimination techniques, and Sturm sequences. The advantages of the design procedure are that it simplifies the control design to managing the roots of some single-variable polynomials while also preserving the controller structure and complying with the necessary and sufficient conditions of stability.