On the Condition of Complete Controllability of Stage-by-Stage Changing Linear Dynamic Systems with Varying Dimension of the Control Vector

Abstract

The control problem of stage-by-stage changing linear dynamic systems with varying dimension of the control vector is considered. A necessary and sufficient condition for complete controllability of the stage-by-stage changing linear non-stationary systems with varying dimension of the control vector is obtained; when the condition is satisfied the system can be transferred from any given initial state specified at the first stage to any final state specified for the last stage with the corresponding control actions. The condition of complete controllability for a stage-by-stage changing linear stationary system is expressed directly through the initial parameters of the system and is comparable with the well-known Kalman condition for the ordinary systems. The qualitative properties of controllability of such systems are revealed.