5Multimodel Control

In recent years, many studies on analysis and synthesis problems have been dedicated to the multimodel approach. This was motivated by the desire to consolidate problems in control law synthesis and in the estimation of the state of nonlinear processes with a digital basis. Such opportunities have become possible because of the multimodel approach and through the development of effective digital resolution tools that are mainly based on convex optimization programs.

Automatic control is based on the concept of models that represent the dynamic behavior of a system. For example, a system can be modeled by a mathematical input–output behavior relationship or by an equation that characterizes its change of state. The dilemma then lies between the fidelity of the model to the process and the adequacy of this model in possessing a mathematically and easily exploitable description. Given the difficulty of the task, the engineer is often required to consider some classes of systems, from physical considerations, that follow structural restrictions (linearity, convexity, etc.), which produce approximations of the model. Thus, linear representations have been widely used. The nonlinear model is represented by a linear model obtained as a first approximation within the vicinity of a given point. The disadvantage of this approach is its uniquely local validity.

To overcome this difficulty, a comprehensive approach was proposed: this was based on multiple models that ...

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