Model Reduction for Linear and Nonlinear Control Systems

As the world grows more complicated so do control systems. In can be very hard to simulate and/or to develop intuition for a complex system described by a high dimensional model so tools have been developed to approximate a high dimensional model by a lower dimensional one. One goal of such an approximation could be that the input to output map of the lower dimensional model should be a good approximation to that of higher dimensional one. Another goal could be that a controller designed for the lower dimensional model should perform satisfactorily for the higher dimensional one.