Auxiliary Function-based Integral/Summation Inequalities: Application to Continuous/Discrete Time-Delay Systems

Abstract

In the field of stability analysis for time-delay systems, finding precise bounds of integral/summationforms of quadratic functions plays a key role in reducing the conservatism. Consequently, there have been manyattempts to develop inequalities yielding much tighter bounds. This paper develops novel inequalities using intermediateterms called auxiliary functions, which includes the existing inequalities as special cases. The stabilityconditions for continuous/discrete time-delay systems are derived in terms of linear matrix inequalities (LMIs) byusing the proposed inequalities with simple numerical examples.