Condition for Sensitivity Unidentifiability of Linear Systems with Affinely Parameter-Dependent Coefficient Matrices

In this paper, we analyze “sensitivity identifiability” of initial states and parameters in affinely parametrized linear systems. If the true parameter is sensitivity unidentifiable (non-SI), optimization-based estimation algorithms may face computational problems. Thus, it is important to detect whether the parameter is non-SI a priori. To this aim, we address a problem to find the condition that the parameter is non-SI for any initial state and input. Then, we obtain a sufficient condition for the problem. The condition is given by algebraic equations and is expected to be the foundation of structural conditions. We show systems that satisfy the condition and are observable and controllable.