The analysis and design of multirate sampled-data feedback systems via a polynomial approach
This thesis describes the modelling, analysis and design of multirate sampled-data feed-back via the polynomial equations approach. The key theoretical contribution constitutes the embedding of the principles underpinning and algebra related to the switch and frequency decomposition procedures within a modern control framework, thereby warranting the use of available computer-aided control systems design software. A salient feature of the proposed approach consequently entails the designation of system models that possess dual time- and frequency-domain interpretations. Expositionally, the thesis initially addresses scalar systems excited by deterministic inputs, prior to introducing stochastic signals and culminates in an analysis of multivariable configurations. In all instances, overall system representations are formulated by amalgamating models of individual sub-systems. The polynomial system descriptions are shown subsequently to be compatible with the Linear Quadratic Gaussian and Generalised Predictive Control feedback system synthesis methods provide causality issues are dealt with appropriately. From a practical perspective, the polynomial equations approach proffers an alternative methodology to the state-variable techniques customarily utilised in this context and affords the insights and intuitive appeal associated with the use of transfer function models. Numerical examples are provided throughout the thesis to illustrate theoretical developments.