The generalized H2 controller synthesis problem of sampled-data systems

This paper tackles the generalized H2 controller synthesis problem of sampled-data systems, which is associated with the controller minimizing the induced norm from L2 to L∞. 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 H2 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 H2 performance for the sampled-data system that is close enough to its optimal generalized H2 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 H2 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 H2 controller synthesis problem. Finally, numerical examples are given to validate the overall arguments. © 2022 Elsevier Ltd