Positive Stabilization for a Class of Separable Positive Nonlinear Systems

This paper considers the problem of positive stabilization for a special class of nonlinear system consisting of a linear part and an additive nonlinearity. The positive nonlinear system is defined in terms of a Metzler matrix associated with the linear part and the nonlinearity is assumed to satisfy the quadratic inequality. First, we provide preliminary results on positive stability for linear systems and generalize it for the special class of separable positive nonlinear systems. Then robust stability is formulated in terms of LMI. Finally, positive stabilization with state feedback is analyzed and a design procedure is outlined which can also be performed through its associated LMI.