An improved stability criterion for networked control systems with a constant transmission delay

This paper proposes a stability criterion for networked control systems with a constant transmission delay by constructing novel Lyapunov-Krasovskii functionals which consist of a continuous functional and a looped-functional. The networked control systems are represented as continuous-time systems with an input delay. In the novel Lyapunov-Krasovskii functionals, the continuous functional utilizes the upper and lower bounds of the input delay for handling the samplings under the transmission delay. The looped-functional uses not only state vectors, but also integral vectors. Also, the proposed looped-functional additionally exploits the interval [t−hk−τ,tk−τ] which is zero at t=tk+1. Furthermore, this paper introduces an additional zero equality for the interval [t,tk+1−τ] by using system dynamics. Based on the novel Lyapunov-Krasovskii functionals and the additional zero equality, an improved stability criterion is obtained in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion.