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The paper is concerned with design requirements when the problem of nonnegative state estimation for one class of uncertain linear Metzlerian time-delay systems with constant delays is tackled, while system states take nonnegative values whenever the initial conditions are nonnegative, the upper and lower system matrix bounds are strictly Metzler matrices, and the upper and lower output matrix bounds are nonnegative matrices. By defining positive definite diagonal matrix variables and introducing an associate structure of linear matrix inequalities, the design conditions are proven, guaranteeing if they are feasible, the resulting observer gain matrix is positive and the reflected observer system matrices are strictly Metzler and Hurwitz. A numerical example illustrates the solvability of the proposed design conditions.

Interval Observer Design for One Class of Uncertain Linear Strictly Metzlerian Time-Delay Systems