On the controllability and observability of linear dynamic systems with variable structure

The paper considers the questions of controllability and observability of linear dynamic systems with variable structure and with conditions of relation on intermediate moments of time. Necessary and sufficient conditions of complete controllability and observability of compounded (and stage by stage changing) linear stationary system are derived. The conditions are expressed directly through the initial parameters of the system and comparisons with the well-known conditions of Kalman are made. It is shown that in separate periods of time the compounded system composed of not completely controllable (or observable) systems with the corresponding intermediate conditions of relations can be completely controllable (or observable) on the entire interval of time. For such a stationary system a conjugate system is considered and an analogy of principle of duality is established, linking the concepts of controllability and observability.