Tracking control of linear time-invariant descriptor systems

Abstract

A feedback design method is developed for input/output tracking control of a class of linear time-invariant descriptor systems. The descriptor systems are decomposed into a dynamic part and a static part. Descriptor-variable feedback is used to simultaneously decouple and stabilize the dynamic part of the system. This can always be done if the dynamic and static parts satisfy separate controllability conditions. Input/output tracking control is then applied to the dynamic part assuming that the output depends on only the decoupled dynamic variables. Perfect steady-state tracking is achieved for smooth inputs if exact knowledge of the system parameters and the descriptor vector is available. The internal dynamics of the closed-loop system are stable if the transfer function is minimum phase. Two examples are included to illustrate the method.