Nice Cross-gramian, the Generalized Symmetry and Determination of Controller Structure for Multivariable Switched Systems

In this paper, the determination of a control struc-ture for discrete-time MIMO switched systems is addressed. In the first step, for discrete-time switched systems, the concept of nice cross-gramians is proposed and investigation is done on whether the suggested nice cross-gramian exists. It has been demonstrated that the nice cross-gramian can be achieved as a solution to a specific algebraic matrix equation, if it exists. While the proposed cross-gramian has a wide range of uses, including model reduction, in this paper, it has been utilized to form the Nice Hankel Interaction Index Array (NHIIA) for control structure selection. The control structure determination strategy which is proposed is one of the few that supports switched systems, takes advantage of gramian-based techniques, and is computationally more effective than its only counterpart.