Finite-time distributed state and disturbance estimation for LTI systems with disturbance: a PEBO-based approach

For a class of linear time-invariant (LTI) systems with disturbance, the finite-time distributed estimation problem of both system state and disturbance was investigated. First, observability decomposition is performed to transform the original system into a cascaded one that is composed of multiple subsystems, and the system disturbance is modelled as the output of an external system. Second, the first substate and external system state are augmented into a new state, and the explicit relationships between state and unknown parameters are established by applying global filtering transformation. Subsequently, the DREM-based parameter estimator and parameter estimation-based observer are developed to simultaneously estimate the first substate and disturbance in finite time. Then, under a unidirectional communication mechanism between adjacent nodes, the subsequent nodes can obtain the estimates of disturbance and substates of all precursor subsystems and only need to estimate the state of current subsystem. Finally, the effectiveness of the proposed methods is illustrated by a numerical example and double-pendulum overhead crane system.