ℋ︁ 2 suboptimal estimation and control for nonnegative dynamical systems

Linear matrix inequalities (LMIs) provide a powerful design framework for linear control problems. In this paper, we use LMIs to develop ℋ 2 (sub)optimal estimators and controllers for nonnegative dynamical systems. Specifically, we formulate a series of generalized eigenvalue problems subject to a set of LMI constraints for designing ℋ 2 suboptimal estimators, static controllers, and dynamic controllers for nonnegative dynamical systems. The resulting ℋ 2 suboptimal controllers guarantee that the closed‐loop plant system states remain in the nonnegative orthant of the state space. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.