Identifiability and Observability of Nonsmooth Systems via Taylor-Like Approximations

New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input–output systems. More specifically, lexicographic derivatives are used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are practically implementable, accurate, and analogous to (and indeed recover) their smooth counterparts. To accomplish this, a novel first-order Taylor-like approximation theory is developed to directly treat nonsmooth (i.e., continuous but nondifferentiable) functions. An L-SERC algorithm is proposed that determines partial structural identifiability or observability, which are useful characterizations in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling.