On finite-time stability and frequency spectrum analysis of the trajectory-based active fault-tolerant control

The aims of this paper are two folds. First, we aim to gain some insights at the time Trajectory-based Active Fault-Tolerant Control (TAFTC) using the frequency spectrum analysis. Secondly, we introduce the concept of finite-time stability (FTS) in the context of AFTC systems. Generally, in TAFTC strategy, the desired specifications are defined in terms of time-domain characteristics under the mathematical framework of behavioral system theory. In this novel fault-tolerant mechanism, we do not work in the traditional input/output setting, i.e. the frequency-domain, at the outset. Instead, we use the system time-trajectories. As an extension, we report some results within this TAFTC strategy showing what frequency-domain properties are actually satisfied by the closed loop. The TAFTC scheme is based on the trajectories generated by the system, where no a priori information regarding the plant is known at a run-time. We use time-limited measurements of the system instead of acquiring a mathematical model of the plant and we deal. Consequently, the theory of FTS renders a more practical insight to study the stability of the TAFTC scheme than is provided by the classical stability theory.