Multirate Nonlinear Sampled-Data Systems: Analysis and Design

This thesis concerns with a common practical problem in the area of sampled-data control systems where the plant is described by nonlinear dynamics and input and output signals are sampled at different rates. We first follow the continuous-time (emulation) approach to propose a general stabilization framework for multirate nonlinear systems in presence of disturbances. This provides a multirate Hinfinity infinity synthesis scheme which can be used to tackle the intrinsic difficulty of unknown exact discrete-time model in nonlinear sampled-data control systems. Moreover, an alternative performance criterion is introduced based on the ℓ2 incremental gain as a stronger form of the usual ℓ2 gain that quantifies whether or not small changes in exogenous inputs such as disturbances or noise will result in small changes at the output.;Finally, in order to verify the advantages of multirate sampling we extend our results to the area of networked-control systems (NCSs). A general output-feedback structure is developed which utilizes the same idea as that of our multirate observer to predict the missing outputs between measured samples. The proposed multirate network-based controller is shown to be capable of preserving the dissipation inequality slightly deteriorated by some additive terms, in spite of network-induced uncertainties and disturbance inputs. By this means a stable NCS can be obtained under much lower data rate and a significant saving in the required bandwidth.;The second part of the thesis investigates the discrete-time approach based on model approximation to the problem of multirate nonlinear sampled-data systems. First, we establish prescriptive design principles for single-rate sampled-data nonlinear observer that is input-to-state stable in the presence of unknown exact discrete-time model as well as disturbance inputs. Our results are then applied to the so-called one-sided Lipschitz nonlinearities to develop constructive design techniques via tractable (linear matrix inequalities) LMIs. Taking the idea of input-to-state stable observer into account, we propose a general framework for multirate observer design that exploits a single-rate observer working at the base sampling period of the system together with modified sample and hold devices to reconstruct the missing intersample signals.