An Improved Quadratic Function Negative Definiteness Lemma for the Stabilization of Nonlinear Cyber–Physical Systems With Actuator Faults

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).