Improved LMI conditions for stability analysis of discrete-time haptic system under time-varying communication delays

The stability analysis of haptic systems without time-delay or with constant time-delay using the frequency-domain criteria such as Routh-Hurwitz or Nyquist has been found in many literatures. However, the stability analysis for the discrete-time haptic systems under time-varying delays remains a major challenge in the field of haptics. Based on the Lyapunov theory, this paper presents a sufficient stability condition in terms of LMI (Linear Matrix Inequality) for the discrete-time systems with an interval time-varying delay. Numerical simulations are included to demonstrate that the proposed condition is less conservative than some existing ones in the literature. The application of the proposed theory to analyze the stability of haptic system is presented in the second part of this paper.