Simultaneous state and fault estimation for positive systems

Abstract

This paper introduces a special type of unknown input observer to estimate the states and faults for linear time invariant positive systems. Both actuator and sensor faults are considered and the solution for each case is provided. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs (disturbances or faults) are present in the systems. To realize simultaneous estimation of states and unknown inputs, we design a positive unknown input observer (PUIO) for positive linear systems. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. The design can be performed with the aid of a positive stabilization procedure via LMI. We also show that the problem of simultaneous states and sensor faults estimations can be solved by a conversion scheme. By introducing an auxiliary positive system constructed from the output and its augmentation to the original positive system, we convert the sensor fault as an unknown input and employ the PUIO design to the augmented system. Finally, theoretical results are supported by numerical examples.