Analysis of \(H_ 2\) and \(H_ \infty\) performance of discrete periodically time-varying controllers
The paper is concerned with \( H_2 \) and \( H_\infty \) performance for discrete linear periodically time-varying (LPTV) controllers for the control of linear time-invariant (LTI) plants. Under some assumptions which, in particular, guarantee that the closed-loop systems controlled by LPTV controllers do not include LTI systems as a subset, it is shown that for \(H_2\) control, an LTI controller can be found to provide strictly better control. A necessary and sufficient condition on the system time-varying response is given. In this case, LTI control can be strictly better than LPTV control. The results provide deeper insight into time-varying mechanism and clarify how the time-varying dynamics can act and degrade the system performance.
scientific article; zbMATH DE number 1038726
scientific article