Fault reconstruction in descriptor linear parameter-varying systems via polytopic unknown-input proportional-integral observers

In this paper, a fault reconstruction scheme for a class of discrete‐time descriptor linear parameter‐varying systems is investigated. A discrete‐time polytopic descriptor linear parameter‐varying system subject to external disturbances and actuator faults is first established; then, using H∞ techniques and regional pole constraints, a novel polytopic unknown‐input proportional‐integral observer is constructed to simultaneously reconstruct system states and actuator faults. Existence conditions for the new polytopic unknown‐input proportional‐integral observer are explicitly derived. The stability and convergence of the presented observer are proved through Lyapunov theory and linear matrix inequalities. Using a slack‐matrix‐variable technique, less conservative results for observer design are obtained. At last, an illustrative example is simulated to verify the effectiveness of the proposed fault reconstruction approach.