H∞$$ {H}_{\infty } $$ Modified Observer‐Based Fault Estimation for Markovian Jump Applied Systems

ABSTRACT This article addresses the fault estimation problem for a class of discrete‐time Markovian jump systems affected by disturbances. A novel modified observer is proposed to simultaneously estimate the system state and fault, considering both constant and time‐varying faults. By constructing a stochastic Lyapunov functional, a sufficient and solvable condition in terms of linear matrix inequalities is established to ensure the stochastic stability of the overall error dynamics system. An performance index is employed to mitigate the effects of unknown disturbances and fault variations. Subsequently, the fault estimation strategy is utilized to address the fault detection problem. Finally, the proposed approach is validated through two practical examples: a boost converter and a mass‐spring‐damper system, illustrating the applicability and feasibility of the theoretical results.