Generalized Hankel Interaction Index Array for control structure selection for discrete-time MIMO bilinear processes and plants

The control technology has been orientated towards decentralized and partially decentralized control strategies. To ensure the success of a decentralized or a partially decentralized control in practice, the first necessary step is to determine a suitable control structure. The control structure selection which is the task of selecting suitable input and output pairs for control design is therefore very important. This paper focuses on control structure selection for discrete-time MIMO bilinear systems. The generalized cross-gramian is introduced in this paper for discrete-time bilinear processes and plants. The existence of the generalized cross-gramian is studied and it is shown that if the cross-gramian exists, it can be obtained by solving a generalized Sylvester equation. To solve the generalized Sylvester equation in a computationally efficient way, an iterative method is developed and presented. The generalized cross-gramians are computed for all SISO subsystems of the discrete-time MIMO bilinear systems. These gramians are used to build the generalized Hankel Interaction Index Array which is used for control structure selection. The proposed method for control structure selection is among the few methods supporting bilinear processes and plants, enjoys the advantages of gramian based methods and it is more efficient in terms of computations compared to its counterparts.