CHARACTERISATIONS OF CONTROLLABILITY FOR VOLTERRA DIFFERENCE EQUATION OF SECOND KIND
Abstract - This paper introduces the characterisation of controllability for the second kind of Volterra difference equations (VDEs). Because controllability is a crucial concept in modern control systems theory, we establish two theorems that characterise the controllability of Volterra difference equations. Control- lability test will be connected to the rank tests of certain matrices: the controllability matrices and also, connected to determinant being non-zero of the controllability Gramian matrix.
Keywords - Volterra Difference Equation, Controllability Matrix, Grammian Matrix, Fundamental Matrix