Stability analysis of time-varying delay system based on a novel generalized integral inequality utilizing finite-interval quadratic polynomial inequalities

This paper proposes an improved stability criterion for time-varying delay system. To reduce the conservatism of the stability criterion, this paper considers the state and its derivative term in a double integral in LKF rather than using the double integral terms with a single state derivative term. By applying a novel generalized free-matrix-based matrix based integral inequality, the use of free matrix is extended. Also, additional matrix variable is introduced in the double integral term which is divided by the time interval. Then, the inequality in terms of the quadratic polynomials is handled to provide the stability criterion in terms of LMIs. We verify the superiority of the proposed criterion by comparing the maximum admissible upper bound of time delay with the literature.