LMI-Based Synthesis of String-Stable Controller for Cooperative Adaptive Cruise Control

Controller synthesis is a challenging problem in cooperative adaptive cruise control (CACC). Especially the requirement of string stability makes it even harder to choose appropriate control parameters. This paper applies a time-domain definition to string stability and converts the problem to the H ∞ control of a time-delay system. Based on the proposed control structure, the $\mathcal H ∞ norm and stability criteria of CACC are satisfied by a set of constraints in terms of a Lyapunov-Krasovskii functional candidate. These constraints are further reduced to linear matrix inequalities so that feasible solutions can be easily and efficiently computed. Simulations on an identified model validate the performance of our method in both frequency and time domains