On State Control of Uncertain Linear Ostensible Metzler Systems

This article deals with state feedback control of uncertain ostensible Metzler systems based on their hidden positive models. To address this problem, an approach is used to formulate stability conditions and parametric boundaries by introducing a decomposition of the ostensible Metzler matrix such that the resulting hidden part in the closed loop is positive and asymptotically stable. The design conditions are provided in terms of linear matrix inequalities with diagonal positive definite matrix variables to comply with the diagonal stabilizability rule. Finally a numerical example is presented to confirm the validity of the analysis result.