Improved stability conditions for time-varying delay systems via relaxed Lyapunov functionals

Abstract

In this paper, the stability analysis of linear systems with time-varying delays is studied. A novel Lyapunov method is presented, in which positive definiteness of the matrices in common Lyapunov functionals is relaxed by adding what is referred to as a zero-integral functional (ZIF). A general form of auxiliary polynomial-based functionals that contains such ZIF is given. Choosing polynomials of different order as well as exploring double-delay-product (DDP) terms, novel Lyapunov functionals are constructed, which contribute to a set of improved stability conditions expressed in terms of linear matrix inequalities. Finally, numerical examples are provided to corroborate the merits of the proposed method relative to a number of existing methods, and in particular, the effectiveness of the proposed ZIFs and DDP terms in reducing the conservatism of stability conditions.

Keywords:

• Time-varying delay
• stability
• relaxed Lyapunov functionals

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant numbers 62088101, 61925303, 62173034, U20B2073, and 61720106011] and in part by the Natural Science Foundation of Chongqing [grant number 2021ZX4100027]. This work was also supported by National Key R&D Program of China [grant number 2018YFB1700100].