On the uniform algebraic observability of multi-switching linear systems

The main objective of this paper is the characterisation of the notion of uniform algebraic observability for multi-switching linear systems. In particular, it is shown that a multi-switching linear system is 'generically' uniformly algebraically observable if and only if the number of available measurements is greater than the number of switching signals acting on the systems. This result is established without requiring any knowledge about the (possibly, stochastic) process generating the switching pattern. Moreover, since such systems can be used to model sensor networks, the results given in this paper can 'generically' be used to design simple observers for sensor networks able to cope with sensor failures and data losses.