ON CONTROLLING GENERALIZED STATE-SPACE (DESCRIPTOR) SYSTEMS

Linear time-invariant control systems of the form Edx/dt equals Ax plus Bu are considered where E and A are not necessarily square matrices. Any vector x(t//0) that can be obtained as a solution of the system for some u(t) and some t equals t//0, is termed an 'admissible initial state' and it is assumed that the system has a unique solution for any input and for any admissible initial state. The problem to be solved is this: find an input u(t) that drives the system from an admissible initial state to a prescribed final state in a given time t//f greater than 0. If the basic assumption regarding uniqueness of solutions holds, the problem of controlling the given generalized state-space (descriptor) system can be reduced to a standard control problem involving an 'ordinary' state-space system of simple form. Then, if the 'ordinary' system is completely controllable, a desired input can be calculated from a well-known formula.