Set-transition observability of switched linear systems

In this paper, we develop and investigate the set transition observability problem for switched linear systems. The set transition (ST) observability problem considers when the set of modes is partitioned into two classes, corresponding for example to safe modes (SM) of operation and failure modes (FM) of operation, as studied herein. The ST observability problem is to identify mode sequence transitions that move from safe to fail from the output of the system given that the system initializes in a safe operating mode. We address the ST observability problem for switched systems with autonomous linear time-invariant (LTI) subsystem dynamics and no state jumps. Beginning in a safe operating mode reflects many system monitoring applications where the system is initialized by a technician or a reset. Applications include stroke and heart attack detection and component failures. The main contribution of this paper is a necessary and sufficient condition for ST observability of switched systems with LTI subsystems.