Polynomials-based integral inequality for stability analysis of linear systems with time-varying delays

This paper employs polynomial functions to extend a free-matrix-based integral inequality into a general integral inequality, say a polynomials-based integral inequality, which also contains well-known integral inequalities as special cases. By specially designing slack matrices and an arbitrary vector containing state terms, it reduces to an extended version of Wirtinger-based integral inequality or the free-matrix-based integral inequality. Numerical examples for stability analysis of linear systems with interval time-varying delays show the improved performance of the proposed integral inequality in terms of maximum delay bounds and numbers of variables.