Minimum sensitivity design via gradient flow techniques

The minimum sensitivity design problem refers to the general systems problem of determining which parameterization of a given mathematical model minimizes the sensitivity of the model´s behavior to perturbations in the parameter values. In specific instances, like the design of linear state space models, the analytical solution to this problem is known. In other cases an analytical solution is intractable, and thus, numerical solutions are sought. In this paper gradient flow techniques are explored in a Riemannian geometry context for application to the general minimum sensitivity design problem. In particular, integrability conditions are developed which when satisfied guarantee the existence of an appropriate gradient flow. The numerical method is demonstrated on a simple state space example where the analytical solution is known