Observer-based fault tolerant control design for periodic piecewise time-varying systems: a fault estimation approach

This study tackles the fault estimation issue for a continuous-time periodic piecewise time-varying systems (PPTVSs) with delays, fault signal and external disturbances. In particular, the PPTVSs are conjured up by segmenting the fundamental period of the periodic system into a finite number of subintervals. Moreover, fault estimator is designed in line with periodic piecewise observer systems to estimate the immeasurable states of the PPTVSs and the fault signal, simultaneously. Subsequently, in accordance with the estimated values of the fault signal and state dynamics, a fault-tolerant controller is devised. Moreover, by utilising Lyapunov stability theory and matrix polynomial lemma, sufficient criteria are procured in context of linear matrix inequalities to affirm the uniform boundedness of the undertaken system and error system. Further, relying on the acquired constraints, the precise configuration of the fault-tolerant control and observer gain matrices are proffered. Eventually, by offering two illustrative examples including mass-spring-damper system, the utility and potential of presented theoretical insights are validated.