Frequency-interval control configuration selection for multivariable bilinear systems

• We introduced frequency-interval gramians for bilinear systems.
• We proposed an interaction measure based on the frequency-interval gramians.
• A method for the control configuration selection based on the proposed interaction measure is proposed.

Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of decoupled (SISO or block) controllers for multivariable systems. This step is an important prerequisite for a successful industrial control strategy. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. First, new frequency-interval gramians are presented for bilinear systems. These gramians are devised in particular for many applications in which one is interested in analysis and control of a system within a frequency-interval. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. These gramians are used in the interaction measure for control configuration selection of MIMO bilinear systems. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure supports bilinear processes, can show the input–output interactions for any frequency-interval of interest, and can be used to propose a richer sparse or block diagonal controller structure.