Complete characterisation of disturbance estimation and fault detection for positive systems

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This study considers the problem of disturbance estimation and fault detection for positive systems. Depending on the occurrences of disturbance and/or faults on positive systems, the authors use two types of observer structures and provide design strategies for reliable estimation of states, disturbance, and faults. Although various positive observers have been designed for positive systems, they fail to estimate the states in presence of unknown inputs. To realise simultaneous estimation of states and unknown inputs for positive systems, a special type of unknown input observer (UIO) called positive UIO (PUIO) is introduced and an linear matrix inequality (LMI) based approach is provided to make its design possible. The authors also show that simultaneous states and sensor fault estimation can be solved by a conversion scheme through a positive filtering process of the output. This allows to convert the sensor fault as an unknown input and employ the PUIO design. Finally, the problem of robust fault detection for positive systems is formulated and solved by combining the capability of UIO with proportional–integral (PI) observer. This integrated observer (PIUIO) decouples the unknown input disturbance through its UIO part while allowing PI part to estimate the fault. Several examples are constructed to support the theoretical results.