  We present a complexity reduction algorithm for a family of
parameter-dependent linear systems when the system parameters belong to a
compact semi-algebraic set. This algorithm potentially describes the underlying
dynamical system with fewer parameters or state variables. To do so, it
minimizes the distance (i.e., H-infinity-norm of the difference) between the
original system and its reduced version. We present a sub-optimal solution to
this problem using sum-of-squares optimization methods. We present the results
for both continuous-time and discrete-time systems. Lastly, we illustrate the
applicability of our proposed algorithm on numerical examples.
