Embeddability of nonlinear discrete equations with variable structure in linear systems (Q2703913)

When dealing with nonlinear systems with discrete-time, the construction of linearization methods has become a rapidly growing field of research both for pure and applied mathematicians.NEWLINENEWLINENEWLINEIn this work, a linearization process, the so-called property of \(p(t)\)-embeddability of discrete equations with variable structure in the class of linear discrete systems is studied. This property was introduced by the second author [\textit{I. V. Gaishun}, Differ. Uravn. 33, 1607-1614 (1997; Zbl 0949.39001)] generalizing to nonlinear systems with discrete-time the problem of embeddability for systems of ordinary differential equations as done in e.g. [\textit{S. P. Banks} and \textit{A. Ashtiani}, Int. J. Syst. Sci. 16, 841-853 (1985; Zbl 0577.93007)].NEWLINENEWLINENEWLINEIn the paper under review, necessary and sufficient conditions are given so that a set of nonlinear discrete equations with variable structure can be embedded in the class of linear finite-dimensional discrete systems. An application for the implementation theory of input-output dynamical systems along with an example of embeddability of discrete Volterra equations are also presented.