Multi-fault estimation of T–S fuzzy chaotic systems based on adjustable order observer

Chaotic systems have attracted significant attention in scientific research and engineering applications due to their unique properties. In this context, this paper investigates a class of T–S fuzzy chaotic systems with unknown inputs and external disturbances. Specifically, it addresses the problem of fault estimation (FE) for process and sensor faults. First, the nonlinear dynamics of the chaotic system are accurately described using the T–S fuzzy model. Building upon this modeling step, an augmented system is constructed by integrating the system states, process fault, and sensor fault into a new state variable. Next, a tunable fuzzy observer design method is proposed, where the observer order can be adjusted within a specified range to achieve an effective trade-off between estimation accuracy and computational cost. Subsequently, based on Lyapunov stability theory, sufficient conditions for the uniform ultimate boundedness (UUB) of the observer error system are derived, and the observer gain matrices are obtained in terms of linear matrix inequalities (LMIs). As a result, the proposed method enables simultaneous estimation of system states, process fault, and sensor fault, where the faults can be either constant or time-varying. Finally, simulations on a chaotic Lorenz system validate the effectiveness, practicality and superiority of the proposed method.