Stability Analysis of Haptic Systems With Time-Varying Delay via a Delay-Product-Type Lyapunov–Krasovskii Functional

In this brief, the stability of the haptic system with a time-varying delay is studied by developing a new stability criterion. Firstly, the haptic system model with a time-varying delay is established. Next, based on the Lyapunov-Krasovskii stability theory, a delay-product-type Lyapunov-Krasovskii functional is constructed. Then, a new delay-dependent stability criterion with less conservatism due to more delay information is derived by applying an auxiliary function-based integral inequality. Finally, a case study is carried out to show the stable boundaries of different delays. The results show that, for the same delay boundary, the stable upper bound of the haptic system increases first and then decreases with the rise of the virtual damping. Moreover, increasing the time delay has negative effects and makes the system unstable.