New double integral inequality with application to stability analysis for linear retarded systems

This paper presents the development of a new double integral inequality (II) with the motivation of yielding quadratic approximation. It is well known that approximating integral quadratic terms with quadratic terms involves a certain degree of conservatism. In this paper, a sufficient gap has been identified in the approximation of two recent IIs reported in the literature, thereby leading to the new double II. The developed inequality has been applied to access the stability of a linear retarded system to estimate a maximum delay upper-bound. Furthermore, a mathematical relationship of the new double II with existing inequalities is discussed to show that the developed inequality is more general, effective and bears less computational burden. Four numerical examples are given to validate the authors' claim with regard to the effective estimate of delay bound results for a linear retarded system.