Recent zbMATH articles in MSC 93B50https://zbmath.org/atom/cc/93B502022-11-17T18:59:28.764376ZWerkzeugThe generalized \(H_2\) controller synthesis problem of sampled-data systemshttps://zbmath.org/1496.930752022-11-17T18:59:28.764376Z"Kim, Jung Hoon"https://zbmath.org/authors/?q=ai:kim.jung-hoon"Hagiwara, Tomomichi"https://zbmath.org/authors/?q=ai:hagiwara.tomomichiSummary: This paper tackles the generalized \(H_2\) controller synthesis problem of sampled-data systems, which is associated with the controller minimizing the induced norm from \(L_2\) to \(L_\infty \). To alleviate the difficulty of the linear periodically time-varying (LPTV) nature of sampled-data systems, we first take an operator-based approach to sampled-data systems via the lifting treatment. We next develop a framework for piecewise constant approximation in the context of the generalized \(H_2\) controller synthesis problem after further applying the so-called fast-lifting treatment. An optimal controller for the approximate treatment is also shown to achieve the generalized \(H_2\) performance for the sampled-data system that is close enough to its optimal generalized \(H_2\) performance, if the fast-lifting parameter \(N\) is large enough. This is established by deriving, in a fashion suitable for controller synthesis, upper and lower bounds on the resulting sampled-data generalized \(H_2\) performance, where their gap tends to 0 at the rate of \(1 / N\). We further introduce a discretization method of the continuous-time plant, with which the controller synthesis in the approximate fashion can actually be carried out through an equivalent discrete-time counterpart of the generalized \(H_2\) controller synthesis problem. Finally, numerical examples are given to validate the overall arguments.