Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate

This work considers the problem of network inference of continuous-time linear dynamical systems
with full-state measurements. This amounts to identification of the matrix A (or the boolean structure
thereof) in the state-space representation. The main motivation for this work are the slow-sampled
dynamical systems in biomedicine applications, where the typical signals also have low signal-to-noise
ratio. For such systems classical identification methods fail to apply. When the sampling frequency is
not high enough, the problem of system aliasing is of importance. A method is proposed that explores
alternative state-space representations due to aliasing. The one with sparest structure is chosen.
Another algorithm is presented, in the case of large noise. In this case the sparse matrix is obtained
by solving a non-convex optimization problem with l1-regularization.