Discrete approximation of continuous-time systems: a survey

A survey of techniques suitable for discrete approximation of continuous-time systems is presented. Most of them are assigned to two groups in which the ℒ-transformation is utilised either directly or indirectly. The direct approach includes the time-response invariance methods, the forming element techniques, the convolution approximation and the stochastic matching methods. From among the indirect procedures, the integrating operator methods distinguish themselves. They can be used in simple or expanded versions. Roots selection and transformations using inverse approximations are also related to the indirect or partial matching technique. There is a class of normal transformations which have the common feature of employing Chebyshev functions. Stable forms of normal interpolators and integrating operators, and a piecewise-normal approximation are useful in the derivation of discrete-time state-space models.