Enforcing Stability of Linear Interpolants in the Loewner Framework

This letter considers the problem of constructing exponentially stable interpolants in the Loewner framework for linear systems of differential-algebraic equations. A designer must solve the static output feedback problem to construct a stable interpolant of minimal order without compromising the interpolation conditions. Yet, this problem is not always solvable even for controllable and observable systems. We provide a motivating example where sets of tangential interpolation data are given for which it is impossible to construct a stable interpolant of minimal order. Following this, two new parameterized families of interpolants are given, which embed an observer with state-feedback into the interpolant. Hence, with the cost of some additional states, the existence of a stable interpolant is guaranteed with standard controllability and observability conditions. Finally, the results are demonstrated by using these new families to construct stable interpolants of the tangential data given in the motivating example.