Design Strategies for Stabilization and Tracking of Positive Singular Systems

Bahram Shafai, Fatemeh Zarei

Abstract: This paper considers the problem of positive stabilization and tracking of linear continuous-time singular systems. First, preliminary results on singular systems are provided. Then, the class of positive singular systems is defined through its equivalent input derivative systems. 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 using its standard representation. It is also shown that the positive stabilization can be achieved by proportional derivative (PD) state feedback by two steps of normalization and subsequent stabilization using LMI. Finally, the proportional integral (PI) feedback is considered for tracking design of positive systems. Numerical examples are included to support the theoretical results.