LEAST-SQUARES PARAMETER-ESTIMATION OF CONTINUOUS-TIME ARX MODELS FROMDISCRETE-TIME DATA

When modeling a system from discrete-time data, a continuous-time para meterization is desirable in some situations, In a direct estimation a pproach, the derivatives are approximated by appropriate differences, For an ARX model this lead to a linear regression, The well-known leas t squares method would then be very desirable since it can have good n umerical properties and low computational burden, in particular for fa st or nonuniform sampling. It is examined under what conditions a leas t squares fit for this linear regression will give adequate results fo r an ARX model, The choice of derivative approximation is crucial for this approach to be useful, Standard approximations like Euler backwar d or Euler forward cannot be used directly, The precise conditions on the derivative approximation are derived and analyzed, It is shown tha t if the highest order derivative is selected with care, a least squar es estimate will be accurate, The theoretical analysis is complemented by some numerical examples which provide further insight into the cho ice of derivative approximation.