Joint Estimation of Continuous and Discrete States in Randomly Switched Linear Systems With Unobservable Subsystems

This article investigates the problem of joint continuous and discrete state estimation of randomly switched linear systems in which subsystems may not be observable. Estimation of both continuous state and discrete sequence simultaneously based on the same output observations is a challenging task that is inherently nonlinear and often infinite dimensional. This article presents necessary and sufficient conditions when joint estimation is possible without using a probing input. When such conditions are not satisfied, a suitably designed input must be used to achieve the goal of jointly detecting the subsystem and estimating the internal state. This article employs certain structures of randomly switched linear systems to develop algorithms that use finite-dimensional estimators for continuous states and sampled data for detecting the discrete states. The convergence analysis shows that this framework can achieve convergence. Examples and simulation case studies are presented to illustrate the main results of this article. The findings of this article can be used to form a supporting foundation for robust control.