Ostensible Metzler Linear Uncertain Systems: Goals, LMI Synthesis, Constraints and Quadratic Stability

This paper deals with the design problem for a class of linear continuous systems with dynamics prescribed by the system matrix of an ostensible Metzler structure. The novelty of the proposed solution lies in the diagonal stabilization of the system, which uses the idea of decomposition of the ostensible Metzler matrix, preserving the incomplete positivity of the system during the synthesis. The proposed approach creates a unified framework that covers compactness of interval system parameter representation, Metzler parametric constraints, and quadratic stability. Combining these extensions, all of the conditions and constraints are expressed as linear matrix inequalities. Implications of the results, both for design and for research directions that follow from the proposed method, are discussed at the end of the paper. The efficiency of the method is illustrated by a numerical example.