This paper proposes a guaranteed cost strategy for longitudinal control of vehicles mainly considering speed-limit control based on map information. Firstly, a state-space model is developed to calculate the desired acceleration for the speed-limit control. Secondly, based on the formulated state-space model, a state-feedback guaranteed cost strategy is developed for the speed-limit control with system uncertainties considered. The stability of the proposed state-feedback guaranteed cost control system is discussed according to Lyapunov stability theory by means of linear matrix inequality approach and Schur complement. Moreover, with the proposed control law, it is proved that the defined cost function has an upper bound. Thirdly, to reduce potential unnecessary acceleration or deceleration caused by disturbances, an event-triggered filter is designed. Finally, to evaluate the performance of the proposed guaranteed cost controller, a switching PID controller, and a guaranteed cost controller without the proposed event-triggered filter are developed for comparisons. The effectiveness and the advantages of the proposed guaranteed cost strategy are proved by simulations where model uncertainties, disturbances, and the latency of the actuator are considered.
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