Finite-Time Distributed State Estimation for Linear Systems With Unknown Inputs via Sliding Modes

This letter presents a design methodology for a robust distributed observer for a class of linear time-invariant systems affected by unknown inputs. The proposed methodology is implemented within a distributed sensor network, allowing for accurate local estimation of the full state after a finite-time transient, even when the system is affected by unknown inputs. The observer utilizes a compensation term based on high-order sliding modes, ensuring that each sensor accurately estimates the locally observable states after a finite-time transient phase. Furthermore, via a consensus-based algorithm, each sensor uses the distributed information to estimate the complete state of the system in finite time.