New results of vehicle sway dynamic system via a new LKF lemma and optimization algorithm

In vehicle systems, both information transmission and motor response exhibit non-negligible time-delay characteristics. To make performance predictions more consistent with actual vehicles, this paper focuses on the conservatism of vehicle delay systems. Existing methods involve strict constraints and limitations, and some approaches exhibit stronger conservatism. Therefore, this paper proposes a new slack Lyapunov function lemma to handle time-delay terms in the system by constructing a relaxation matrix. Additionally, a genetic algorithm is employed to optimize the adjustable parameters in the quadratic function negative determination lemma, further reducing the conservatism of the linear matrix inequality. Based on these strategies, stability criteria for the Takagi-Sugeno fuzzy vehicle sway system are developed. Simulation results demonstrate that the proposed method increases the system's maximum time-delay upper bound, reduces conservatism, and verifies the effectiveness and feasibility of the proposed approach.