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.