On identification of parameterized switched linear systems

Motivated by applications in fault/attack detection of engineering systems, we formulate in this paper a parameterized switched linear systems identification problem. First, we show that the identifiability of parameterized switched linear systems is equivalent to the global identifiability of a parameterized linear time-invariant system. We propose a new necessary and sufficient condition to check the identifiability of a parameterized linear time-invariant system. Second, using the prior knowledge that the difference between the nominal system and the perturbed system is small (with only a small number of parameters that have been changed), we formulate the fault localization problem as a sparse linear regression problem. We investigate the performance of the proposed algorithm when there is a finite number of samples, and propose a necessary and sufficient condition to determine the number of samples required to achieve a “close-to-true” solution. Potential applications of this work can be: a) development of a sensor placement strategy as well as a real-time monitoring algorithm for the early detection of faults (e.g., material aging, line tripping) or attacks in power grids; b) understanding the functionality of genes, proteins and metabolites in disease dynamics, which could potentially lead to early disease detection and drug design.