STABILITY-TESTS AND PERFORMANCE BOUNDS FOR A CLASS OF 2D LINEAR-SYSTEMS

Repetitive, or multipass, processes are a class of 2D systems characte rized by a recursive action with interaction between successive output s or pass profiles. This interpass interaction is the source of the un ique control problem for these processes in that it can cause the outp ut sequence to exhibit oscillations which increase in amplitude from p ass to pass. Previous work has developed an abstract stability theory and applied it to subclasses, such as discrete nonunit memory linear p rocesses which are considered here, to produce basic stability tests. This article begins by reviewing the known stability tests and conclud es that, at best, they only produce highly qualitative indicators of r elative stability and performance. Hence, unlike (say) Bode and Nyquis t tests for standard linear systems, they are of limited appeal as a b asis for computer-aided control systems design. To remove this difficu lty, step response data is used to develop new simulation-based tests which yield, at no extra cost, unique computable performance measures. Further, the undoubted advantages of having such measures available i s clearly shown by developing a (virtually) complete solution to contr oller design for one subclass.