Novel stability criterion for linear system with two additive time-varying delays using general integral inequalities

The stability analysis strategy for continuous linear system with two additive time-varying delays is proposed in this paper. First, for the purpose of analysis, the novel Lyapunov-Krasovskii functional (LKF) consisting of integral terms based on the first-order derivative of the system state is constructed. Second, the derivative of LKF is estimated by utilizing the Wirtinger-based integral inequality and extended reciprocally convex matrix inequality. The delay-dependent stability criterions are established in terms of linear matrix inequalities (LMIs) framework. The results show that the system performances are improved based on both enlarging the maximum allowable upper bound of the time-delays and reducing the number of decision variables. Furthermore, the conservatism of obtained delay-dependent stability criterion is reduced. Finally, a numerical simulation is given to demonstrate the effectiveness of obtained theoretical results.

Automated summary

This paper proposes a stability analysis strategy for continuous linear systems with two additive time-varying delays. A novel Lyapunov-Krasovskii functional (LKF) is constructed for analysis, and the derivative of LKF is estimated using specific inequalities. The delay-dependent stability criteria are established within a linear matrix inequalities framework.