Abstract: Aiming to analyze the effect of time-delay on the quality of magneto-rheological semi-active suspension control system, which exists in control input channel, a novel quarter vehicle magneto-rheological semi-active suspension model with time-delay is build. According to the time-delay differential equation and the variable structure control theory, a time-delay dependent sliding mode controller is designed, which transfers the factors of system time-delay stability to feasible linear matrix inequality analysis through theory deduction and LMI method. The problem of solving maximum margin time-delay can be changed to acquire the minimum value of generalized eigenvalue. Both desktop simulation with Matlab/Simulink and bench experimental results show that, in the scale of system margin time-delay, time-delay dependent sliding mode controller will guarantee the stability of system from the root. It can also weaken the influence of time-delay on the system control quality, so as to improve the vehicle ride comfort.

Key words: Linear matrix inequality, Magneto-rheological damper, Semi-active suspension, Time-delay dependent sliding mode control