General Performance Indices for the time and Frequency Response for the Free Motion of Linear Discrete Control Systems

Abstract

A method for evaluating general performance indices for the time and frequency response for the free motion of a linear stationary discrete control system described by the matrix equation is given. A matrix B is formed from the system matrix A. The transpose of the inverse of the matrix B and its powers is then used to evaluate the expressions and where is a quadratic algebraic form, Δ m is the mth forward difference, and r = 0, 1, 2, …. From these expressions performance indices for the time and frequency response were then determined.