Validated discretization and robust controller design for nonlinear sampled-data control

Sampled-data control of a polynomial nonlinear plant is considered with performance guarantee. In particular, a given continuous-time nonlinear plant is approximately discretized with an explicit error bound and a discrete-time controller is designed so as to be robust against the error bound. Discretization with an error bound is based on a technique from validated computation and robust controller design is based on a linear-like representation. An advantage of this approach is that the design can be made with respect to the quadratic control performance, for example, and the performance is guaranteed for a given sampling time. It can also take into account the intersample behavior of the system. The proposed approach is applied to a simple example and shows its efficacy.