A Direct Algebraic Approach to Design State Feedback and Observers for Singular Systems

Abstract

This paper considers the stabilization problem of singular systems represented by an equivalent system involving input derivatives. Stabilization is achieved by eigenvalue assignment after a subsequent elimination process of input derivatives. First, the connection between the class of systems with derivative inputs and singular systems is analyzed. Then an elimination procedure for input derivatives is given, which transfers the derivative terms from the state equation to the output equation allowing stabilization by state feedback to be performed under a modified controllability condition. The design of observer for the transformed system with input derivatives appearing in the output equation is also considered. It is shown that a similar elimination process can be performed directly in the design procedure of the observer. An immediate benefit of the new approach is the fact that it can be employed to systems that naturally admit input derivatives in their state space models. This is further elaborated in the paper and illustrated as part of design examples.