State-space determination of linear system uncontrollability

State-space representation and analysis of dynamical systems has led to new concepts, one of which is controllability. The origin, definition, and development of the concept of controllability are explored. The concept is used to investigate the conditions of uncontrollability of a typical linear system. Results are given a geometrical interpretation which facilitates visualization of the effect on system controllability of the variation of parameters which characterize the system. Comparative methods are briefly discussed. The discussion demonstrates the correspondence of cancellations in the classical transfer function with determined conditions of uncontrollability. Numerical examples are provided to clarify the more abstract thesis discussions and to test thesis results.