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.

This paper introduces a subclass of positive systems involving input derivatives, which we formally define it as input derivative positive systems. Due to the presence of input derivatives, we provide an algebraic transformation to eliminate the derivative inputs to accommodate the process of stabilization by state feedback. This elimination transfers the input derivative in the output equation, which does not interfere with the design process. Stabilization of input derivative positive systems is performed through its equivalent transformed positive systems in standard form using LMI. To take advantage of this stabilization process, we utilize it for stabilization of positive singular systems. Consequently, we analyze singular systems and its equivalent transformations, which admit derivative input. Thus, algebraic transformation is employed to eliminate these derivative inputs. Finally, we establish the connection between stabilization of positive singular systems and stabilization of input derivative systems by a modified LMI. Numerical examples are included to support the theoretical result.