Delays-dependent region partitioning approach for stability criterion of linear systems with multiple time-varying delays

• Published in: Automatica (Oxford) Vol. 87; pp. 389 - 394
• Main Authors: Ko, Kab Seok, Lee, Won Il, Park, PooGyeon, Sung, Dan Keun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2018
• Subjects: Delayed linear system; Linear matrix inequality; Multiple time-varying delays; Linear matrix inequality; Multiple time-varying delays; Delayed linear system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2017.09.003

This paper considers a delay-dependent stability criterion for linear systems with multiple time-varying delays. To exploit all possible information for the relationships among the marginally delayed states (x(t−τiM),x(t−τi+1M)), the exactly delayed states (x(t−τi(t)),x(t−τi+1(t))), and the current statex(t) for each pair(i,i+1) of time-varying delays, a delays-dependent region partitioning approach in double integral terms is proposed. By applying the Wirtinger-based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning, a stability criterion is derived in terms of linear matrix inequalities. Numerical examples show that the resulting criterion outperforms the existing one in literature.