Controllability and minimum energy control problem of two-dimensional continuous-time fractional linear systems

The effectiveness of this paper lies in a new formulation and solution of the minimum energy control problem for the fractional two-dimensional systems described by the Fornasini-Marchesini first models. The problem of controllability and minimum energy control of a general fractional two-dimensional Fornasini-Marchesini model is newly considered by the authors in this work. Necessary and sufficient controllability conditions are then established using the Gramian matrix. To carry out this study, a new test was described and used in order to give the existence conditions of the solution to the minimum energy control problem and the procedures for calculating an input minimising the given performance index. The usefulness and the precision of the proposed procedure is demonstrated by a numerical examples, Darboux equation and metal rolling process model as a practical application.