Constructive method of investigation of linear compound systems control problems

The paper considers mathematical model of linear compound systems control, described by different differential equations on different time intervals and by some finite conditions for continuation of compound systems motion. Analytical form of compound systems motion is constructed; the properties of motion and geometrical structure of attainability domain are investigated. Necessary and sufficient conditions for complete controllability are formulated. The method of solution of compound systems control problem and the way of solution of optimal control problems are suggested. Existence conditions for program control and motion are formulated.