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Constraint handling is an everyday problem for the control engineer. This book is concerned with constraint handling for systems that are described by a Non-Minimal State Space (NMSS). Such NMSS models are formulated directly from the measured input and output signals of the controlled process and the state vector is directly available without the need to design and implement a state observer. The technique that is studied is Model Predictive Control which a very common when dealing with constraints. New NMSS/MPC control structures are presented in this book for both linear and non-linear systems. For the description of non-linear systems, State Dependent Parameter models are used that are a direct extension of linear NMSS state space models for non-linear systems. The analysis presented should help us understand the structural differences among different controllers for constraint handling and give directions for choosing the most appropriate one. This book should be especially useful to researchers in the area control, constraint handling systems and Model Predictive Control. It is also written in a way to support practicing control engineers with constraint handling techniques.