Squaring-Down Descriptor Systems: Constructive Solutions and Numerical Algorithms

We consider the problem of squaring-down a general descriptor linear time-invariant system. Squaring-down consists in finding a pre- and a post-compensator such that the system is turned into a square invertible one. We consider three classes of solutions: static, dynamic, and norm-preserving. All characterization are made by using generalized state-space realizations while the associated computations are performed by employing orthogonal transformations and standard reliable procedures for eigenvalue assignment. Usual benefits of classical squaring-down schemes like the stability of the designed compensators or preservation of minimum phase, stabilizability, detectability, and the infinite zero structure of the original system are recovered as well.