Characterization of input-output group decoupling for linear descriptor systems using controllability subspaces

In this paper we study the problem of the characterization of group decoupled system for linear descriptor systems with index one using controllable subspaces. From the standard decomposition form, the linear descriptor systems can be separated into slow and fast subsystems. In this form, using controllable subspaces, we give some results for the characterization of input-output group decoupled for slow and fast subsystems, respectively. Furthermore, the characterization of the input-output group decoupling yields the normal forms for the input-output group decoupling of linear descriptor system with index one. This normal form can be used in order to define weakly coupled linear systems. All the results that have been obtained in this study can be used to determine the formulation of algorithms in solving the problem of linear quadratic optimal control that contains systems that are consider as weakly coupled subsystems.