Anticipatory lD and 2D Linear Systems

Notions of anticipaton systems for discrete-time and continuous-time lD linear systems and 2D discrete linear systems are introduced. A discrete-time system is called anticipatory if its state vector and output vector depend on the future values of inputs. A continuous-time system is called anticipatory if its state vector and output vector depend on the derivatives of inputs. Necessary and sufficient conditions for the anticipation of singular discrete-time and coutinuous-time l-D linear systems are established. It is shown that the discrete-time system obtained by discretization from continuous-time one is anticipatory for any value of the discretization step if and only if the continuous-time system is anticipatory. Necessary and sufficient conditions for the anticipation of the singular 2D Fornasini - Marchesini model and the singular 2D Roesser model are established.