Weighted performance criteria for the synthesis of discrete systems

For the free and forced motion of an asymptotically stable linear stationary discrete control system of order , Performance Indexes given by the general expressions and where is any -transformable function, is a vector whose elements are products of the state variables of the system in the form and Δ^mis the th forward difference, can be computed from the system\´s parameter without obtaining an explicit solution of the response. This is achieved by the introduction of a matrix formed in a certain manner from the system\´s matrix and the introduction of a "Matrix -transform" of .