Abstract
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 Déscartes'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.
Keywords
multiple time-delay systems, delay-independent stability, controller synthesis, iterated discriminant
Publisher
IFAC
Publication Date
1-1-2010
Rights Information
Copyright © IFAC 2010
Rights Holder
IFAC
Recommended Citation
Delice, Ismail Ilker and Sipahi, Rifat, "Controller design for delay-independent stability of multiple time-delay systems via Déscartes's rule of signs" (2010). Mechanical and Industrial Engineering Faculty Publications. Paper 47.
Notes
Paper presented at the 9th IFAC Workshop on Time Delay Systems (Czech Republic, 2010). DOI:10.3182/20100607-3-CZ-4010.00027