A new approach for designing a reduced-order controller of linear singular systems

An approach for designing a multivariable reduced-order controller of a linear, time-invariant, singular system is presented. The approach is based on decomposing the original system into slow and fast subsystems using the Drazin inverse technique. The resulting subsystems are then used to obtain an observer of reduced order. This, in turn, it used in designing a new reduced-order controller which is capable of placing the dominant eigenvalues of the system in arbitrary locations. The technique is shown to overcome some difficulties inherent in other treatments of reduced-order controllers of singular systems and assures that the known corresponding controller of the regular state-space systems is merely a special case of the present results