Nonadaptive Distributed State Estimation for Discrete-Time Jointly Observable Uncertain Linear Systems

This paper investigates the distributed estimation problem for discrete-time uncertain linear time invariant systems under the joint observability condition. The problem is highly challenging and remained unresolved until it was recently addressed by an adaptive approach. This papersolvesthisproblemusinganonadaptive approach that introduces new features. An observability transformation is first introduced to decompose the uncertain system, thereby facilitating the parameter and state reconstruction by the two nonlinear mappings. Then, a novel class of distributed nonadaptive observers is pro posed, composed of a nonlinear distributed Luenberger type observer dynamics and two nonlinear mappings. By Lyapunov stability analysis and nonlinear mappings recon struction, we show that the parameter and state estimation are achieved asymptotically for discrete-time jointly observable uncertain linear systems. The proposed nonadaptive scheme enriches design tools for robust control, and circumvents the convergence and stability issues inherent in adaptive approaches as well. Besides, the observer is fully distributed, requiring only local measurements and neighbor-to-neighbor communication, which ensures computational efficiency and scalability.