Multiple-integral inequalities to stability analysis of linear time-delay systems

This paper is concerned with the stability analysis of linear systems with constant delay. First, with the help of Schmidt orthogonalization, we define a new set of orthogonal polynomials. By using the orthogonal polynomial set, we propose a novel multiple-integral inequality, which can achieve less conservatism than many existing inequalities, such as Jensen׳s single-integral inequality, Jensen׳s double-integral inequality, the Wirtinger-based single-integral inequality and the auxiliary function-based double-integral inequality. Then, based on the proposed inequality, we derive a stability criterion for the system under consideration, which is less conservative than the existing ones. Finally, we provide a numerical example to illustrate the effectiveness of the derived criterion.