Structural properties of linear systems

The aim of the thesis is to examine a number of properties related to the set of invariants of linear dynamical systems under different types of transformations and for both state space and transfer function representations. The general objectives have been to classify the invariants according to their generic, non-generic nature, establish links between different types of invariants and system properties and explore the nature and formation of invariants on interconnected systems. More specifically, state space invariants have been classified according to genericity, non-genericity using generic properties of matrix pencils and generic values of controllability, observability indices have been worked out using the generic properties of piecewise Arithmetic Progression Sequence. Similar classification results have been obtained for transfer function models. Some new results on the importance of Plucker invariants have been derived and new tests for controllability, observability were obtained in terms of the rank properties of appropriate controllability-, observability Plucker matrices. Finally, the relationship between the invariants of composite system structure and the invariants of the subsystems has been examined. In particular, it has been shown that under general assumptions on the system structure composition, the zeros of the composite system as well as controllability-, observability indices and decoupling zeros are simply the aggregate of the corresponding subsystem in-variants. The effect of loss of input, output channels on the nature of the invariants of the composite system has also been examined