Observability conditions of switched linear singular systems

The observability problem of switched linear singular（SLS） systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.

Multi-Robot Cooperative Localization:Time-Varying Unobservable Subspace Analysis and Consistent Algorithm Design

This paper investigates the problem of cooperative localization(CL)for a multi-robot system(MRS)under dynamic measurement topology,which involves a group of robots collectively estimating their poses with respect to a common reference frame using ego-motion measurements and robot-to-robot relative measurements.The authors provide a theoretical analysis of the time-varying unobservable subspace and propose a consistent cooperative localization algorithm.First,the authors introduce the relative measurement graph(RMG)to represent the relative pose measurements obtained by the MRS at each instant.Then,the authors derive the local observability matrix over a time interval.An equivalent relationship is established between the local observability matrix and the spectral matrices of the RMG.Moreover,the authors present a method for constructing the unobservable subspace based on the RMG under different topology conditions.Based on this analysis,the authors design a consistent cooperative localization algorithm that satisfies the constraints of the time-varying unobservable subspace.An analytical optimal solution is derived for the constrained optimization problem.Monte Carlo numerical simulations are conducted to demonstrate the consistency and accuracy of the proposed method.