Time-Varying State Space Realizations
Time-varying systems provide an especially fruitful point of view for the study of the properties of linear maps and operators acting on sequences of data vectors. The notation and preliminary results given in chapter 2 prepared the grounds for a realization theory of such systems. A linear operator may often be decomposed into a composition of local linear transformations in which intermediate data called states are generated for use in subsequent stages. This brings the theory of such transformations into the realm of linear dymamic system theory for discrete-time signals. The global transformation plays the role of input-output operator or transfer operator,while the decomposition can be interpreted as the realization of a computational scheme in which small local transformations are executed. Hence, methods from system theory can be used to yield schemes of minimal complexity, optimal approximations to systems of lower complexity, and so on.
KeywordsSingular Value Decomposition Transfer Operator Hankel Operator Hankel Matrix Minimal Realization
Unable to display preview. Download preview PDF.