System decompositions for the design of constrained control systems and its application to the model predictive control

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Model Predictive Control (MPC) has become a standard control strategy for constrained multivariable systems and, for the application to the broader class of mechatronics systems, fast computation algorithm for the online-optimization of control input has been required.In this study, a system decomposition method is derived for linear time-invariant systems and it is clarified that the dominant system responses are fairly characterized based on the eigenvalue problem of compact operators. The fundamental result obtained here is employed for the derivation of low-order MPC control law and the feature of the proposed control law is investigated with several design examples.