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## Relevant tools for dynamic decoupling

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This chapter presents multivariable dynamical system and improvement in the decoupling of multiple-input multiple-output (MIMO) systems in the presence of different types of constraints, that is, to reduce interactions among the loops as much as possible when the plant under control is subjected to either physical, structural or dynamic constraints. First, we recall some basic concepts of MIMO systems analysis. Then, the affine parameterisation of all the controllers which internally stabilise the feedback system is introduced, together with the closely related Internal Model Control (IMC). Based on this control strategy, some design procedures are described in order to achieve the dynamic decoupling of stable minimum phase (MP) systems, non-minimum phase (NMP) systems and unstable systems. Finally, the effects and limitations of diagonal (full) dynamic decoupling in systems with right-half plane (RHP) zeros are briefly discussed.

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