On the numerical computation of a structural decomposition in systems and control

In this paper, we develop a new numerical method for a special coordinate basis of a linear time invariant system. Such a special coordinate basis is essentially a structural decomposition which explicitly displays the finite and infinite zero structures, as well as the invertibility structures of the given system. The technique is playing important roles in numerous topics in system and control theory, such as robust control, H_∞ and H₂ optimal control almost disturbance decoupling, and zero placement of linear systems, just to name a few. Our method consists of three steps: reduction by orthogonal transformations, reduction by generalized Sylvester equations, and extraction of infinite zero structure. The performance of our method is illustrated by some numerical examples.