A Distributed Observer for a Time-Invariant Linear System

Abstract

A time-invariant, linear, distributed observer is described for estimating the state of an $m>0$ channel, $n$-dimensional continuous-time linear system of the form $\dot{x}=Ax,y_i=C_{i}x,i\in \{1,2,\cdots ,m\}$. The state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives the state $z_j$ of each of its neighbors' estimators. Neighbor relations are characterized by a constant directed graph $\mathbb{N}$ whose vertices correspond to agents and whose arcs depict neighbor relations. The overall distributed observer consists of $m$ linear estimators, one for each agent; $m-1$ of the estimators are of dimension $n$ and one estimator is of dimension $n+m-1$. Using results from classical decentralized control theory, it is shown that subject to the assumptions that (i) none of the $C_i$ are zero, (ii) the neighbor graph $\mathbb{N}$ is strongly connected, (iii) the system whose state is to be estimated is jointly observable, and nothing more, it is possible to freely assign the spectrum of the overall distributed observer.

8 pages, 1 figure

Cited by in corpus (14)

• Functional observability and target state estimation in large-scale networks
• Combining Federated Learning and Control: A Survey
• A Distributed Observer for a Continuous-Time Linear System with time-varying network
• Small-gain theorem for stability, cooperative control and distributed observation of infinite networks
• Fixed-Time Convergent Distributed Observer Design of Linear Systems: A Kernel-Based Approach
• Towards a minimal order distributed observer for linear systems
• Decentralized Secure State-Tracking in Multi-Agent Systems
• Decentralized Design and Plug-and-Play Distributed Control for Linear Multi-Channel Systems
• Distributed Feedback Control of Multi-Channel Linear Systems
• A simple approach to distributed observer design for linear systems
• Distributed Control of Linear Multi-Channel Systems
• A Distributed Observer for a Discrete-Time Linear System
• H2 and H-infinity Suboptimal Distributed Filter Design for Linear Systems
• Accelerating Distributed SGD for Linear Regression using Iterative Pre-Conditioning