Temporal solution-based output observer design for single output LTI systems

In this paper, we present an output observer for single output linear time invariant (LTI) systems based on the temporal state solution of the system. The aim of an output estimator/observer is to reconstruct the output of the system for various purposes, namely fault detection, filtering and output stabilisation among others. A distinctive feature of this observer is that time variable is used as input in the observer equation. Proper transformations are employed to avoid the inversion of large matrices involved in the system's solution computation. Numerical simulations are presented with and without noise presence.