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, Δm is the mth forward difference, and r = 0, 1, 2, …. From these expressions performance indices for the time and frequency response were then determined.
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References
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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.