Controller Design for Delay-Independent Stability of Multiple Time-Delay Systems via DéScirctes's Rule of Signs

A general class of multi-input linear time-invariant (LTI) multiple time-delay system (MTDS) is investigated in order to obtain a control law which stabilizes the LTI-MTDS independently of all the delays. The method commences by reformulating the infinite-dimensional analysis as a finite-dimensional algebraic one without any sacrifice of accuracy and exactness. After this step, iterated discriminant allows one to construct a single-variable polynomial, coefficients of which are the controller gains. This crucial step succinctly formulates the delay-independent stability (DIS) condition of the controlled MTDS based on the roots of the single-variable polynomial. Implementation of the DéScirctes's rule of signs then reveals, without computing these roots, the sufficient conditions on the controller gains to make the LTI-MTDS delay-independent stable. Case studies are provided to demonstrate the effectiveness of the proposed methodology.