On the design of time-varying, linear closed loop systems with the aid of a new transform technique

Methods for employing a new transform technique for the design of feedback control systems for linear, time-varying, discrete-time systems are presented. Assuming that the operation of a plant can be characterized by an
N\timesN
matrix
P
, the transform technique, is based on the decomposition of
P
in the form
P = (Y \Delta f)\LambdaX^{T}
, where X
^T
is an
N\timesN
matrix which acts as a direct transform, Λ is an
N\timesN
diagonal matrix which acts as a transfer function, and (
Y \Delta f
) is an
N\timesN
matrix which acts as an inverse transform. System matrices
G
and
H
, for the cascade and feedback parts of a compensation system, are selected through a consideration of the desired closed loop system response and the desired closed loop system sensitivity to changes in plant parameters. It is shown that the transform technique allows this design to be carried out with relatively straightforward calculations which yield insight into system behavior at each stage. Use of this design procedure is illustrated with a significant example