Standard mathematical models: Behavioral methods in control

A fundamental problem in science and engineering is to predict the effect a particular action will have on a physical system. Engineers use many different kinds of models to predict the results of applying inputs to physical systems. The fundamental idea behind input–output models is to try to model only the relation between inputs and outputs. Electronic amplifiers are often described only by input-output models. It is useful to generalize the simple electronic example to a large class of single-input single-output models. The development of the continuous-time impulse response as an input-output model for linear invariant and time invariant (LTI) continuous-time systems is analogous to that for discrete time. A natural beginning is with the second key to an economical description of LTI systems, the definition of the unit impulse. The other common form for LTI input–output models is the transfer function