Finite time stability of linear time varying delay systems using free matrix based integral inequalities

Abstract

This paper discusses the problem of finite time stability (FTS) for linear delayed systems where the time-varying delay is bounded. First, based on a Lyapunov–Krasovskii Functional (LKF) which contains terms of triple integrals, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, new approximations of the single and multiple quadratic integrals that appear in the LKF derivative are established using integral inequalities, called free-matrix-based integral inequalities. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore more effective. Finally, less conservative design conditions in terms of Linear Matrix Inequalities (LMIs) are proposed and solved by the LMI Tools of MATLAB to show the advantage and effectiveness of the proposed approach.

Keywords

• Finite time stability (FTS)
• Linear systems
• Time-varying delay
• Triple integrals
• Free-weighting matrices