Stochastic Observability and Convergent Analog State Estimation of Randomly Switched Linear Systems With Unobservable Subsystems

This article investigates observability and observer design for randomly switched linear systems (RSLSs) whose subsystems are all unobservable. Conditions for determining the analog state uniquely during operation, defined as stochastic observability, are studied. This article establishes probabilistic descriptions of stochastic observability for fast switching RSLSs. Design methods for subsystem observers and their organization for estimating the entire state are introduced. Convergence properties are established, including strong convergence and exponential convergence rate. Estimation error probabilities under finite data are derived by using the large deviation principles. Some critical structural conditions are characterized that permit organization of subsystem observers for achieving a convergent observer for the entire state. Examples and simulation case studies are presented to illustrate the main results of this article.