Design of H-/H∞ based fault detection filter for linear uncertain systems using linear matrix inequalities

Abstract

One of the significant challenges in model-based fault detection is achieving robustness against disturbances and model uncertainties while ensuring sensitivity to faults. This study proposes an optimized approach for designing fault detection filters for discrete-time linear systems with norm-bounded model uncertainties. The design leverages the H-/H∞ optimization framework and is expressed through linear matrix inequality constraints. The filter is designed to produce a residual signal that balances two opposing objectives: minimizing the impact of disturbances and model uncertainties while maximizing fault sensitivity. The effectiveness of the proposed method is demonstrated through simulations involving sensor and actuator fault detection in the well-known three-tank system. Simulation results illustrate the method's ability to maintain robustness against disturbances and uncertainties while effectively detecting faults in the system.