Balancing related methods for minimal realization of periodic systems

We propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time-varying dimensions. The first method belongs to the family of square-root methods with guaranteed enhanced computational accuracy and can be used to compute balanced minimal order realizations. An alternative balancing-free square-root method has the advantage of a potentially better numerical accuracy in case of poorly scaled original systems. The key numerical computation in both methods is the solution of nonnegative periodic Lyapunov equations directly for the Cholesky factors of the solutions. For this purpose, a numerically reliable computational algorithm is proposed to solve nonnegative periodic Lyapunov equations with time-varying dimensions.