A delay decomposition approach to robust stability analysis of uncertain systems with time-varying delay

This paper is concerned with delay-dependent robust stability for uncertain systems with time-varying delays. The proposed method employs a suitable Lyapunov–Krasovskiiʹs functional for new augmented system. Then, based on the Lyapunov method, a delay-dependent robust criterion is devised by taking the relationship between the terms in the Leibniz–Newton formula into account. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.