Realisation theory for dynamical systems

The paper is concerned with certain aspects of modelling dynamical systems. This problem can be divided into two parts; first, there is the question of identifying the system structure, and secondly of identifying the parameters defining the structure. Realisation theory provides a framework in which models of dynamical systems can be analysed mathematically, and in particular affects the structural identification problem. This paper is an expository paper devoted to surveying the main results. Three main areas are treated, those of linear, bilinear and nonlinear systems, providing a natural progression of technique and applicability. The complexities of the nonlinear theory have been minimised as far as possible, so that the results can be applied with a limited knowledge of calculus and algebra. Examples on Hamiltonian and polynomic systems are included to show how realisation theory is used in structural identification.