Positive Stabilization and Observer Design for Positive Singular Systems

Bahram Shafai, Fatemeh Zarei

Abstract: This paper considers the class of positive singular systems and provides a new approach to achieve stabilization and observer design with positivity constraints. First, the connection between singular systems and its equivalent input derivative systems is established and their positivity with stability properties are analyzed. Then, an algebraic transformation is introduced, which allows to eliminate the derivative inputs and to obtain an equivalent standard system. A careful mathematical derivation was performed to obtain closed-form expressions for the coefficient matrices of the resulting transformed system. Consequently, the design of positive stabilization of positive singular systems was made possible using the equivalent standard state space representation. Finally, the design of positive observer for positive singular system is provided. It is shown that a similar procedure is required to eliminate the input derivatives that appear in the output equation allowing the observer to be designed. Both positive stabilization and positive observer designs are formulated and solved in terms of LMIs.