An Improved Quadratic Function Negative Definiteness Lemma for the Stabilization of Nonlinear Cyber–Physical Systems With Actuator Faults
针对含执行器故障的非线性信息物理系统，提出一种改进的二次函数负定性引理，通过划分时滞区间并利用切线交点导出线性矩阵不等式条件，实现系统渐近镇定，并在自主地面车辆仿真中验证了有效性。
This article deals with the stabilization of nonlinear cyber-physical systems (CPS) subject to actuator faults via the fault-tolerant control (FTC) algorithm. First, to tackle the time-varying delays taken into the system, we proposed a novel quadratic function negative determination lemma, which derives the sufficient conditions for the corresponding quadratic polynomials arising in the derivatives of Lyapunov-Krasovskii functional (LKF). For this purpose, we are parting the time-delay intervals into uniformly equal subintervals and the tangents intersection is carried out in the region of each partitioned intervals. Thereafter, from the cross-points of tangents in each subinterval and choosing a freely adjustable parameter within the delay bounds, we attained a novel quadratic function negative definiteness conditions which profits with high system performance. By means of Lyapunov stability theory (LST), the sufficient conditions are derived in the form of linear matrix inequalities that ensure the asymptotic stabilization of the addressed system. Finally, numerical simulations including the realm of autonomous ground vehicle (AGV) problem are performed, and the comparative analysis in the line of negative-definite (ND) lemmas is exhibited to showcase the efficacy of the proposed approach (PA).