Multirate Nonlinear Sampled-Data Systems: Analysis and Design

• Author / Creator

  Beikzadeh, Hossein

• 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 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 L_2 gain that quantifies whether or not small changes in exogenous inputs such as disturbances or noise will result in small changes at the output.

  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.

  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.

• Subjects / Keywords

  • Sampled-data control
  • Nonlinear systems
  • Multirate sampling

• Graduation date

  Spring 2014

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3X389

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.