Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance

Mathematical models of dynamic systems are required in most areas of scientific enquiry and take various forms, such as differential equations, difference equations, state-space equations and transfer functions. The most widely used approach to mathematical modelling involves the construction of mathematical equations based on physical laws that are known to govern the behaviour of the system. Amongst the drawbacks to this approach are that the resulting models are often complex and not easily estimated directly from the available data because of identifiability problems caused by over-parameterisation. This complexity also makes them difficult to use in applications such as control system design.

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