LMI Approach in State Control Design for Uncertain Positive Time-Delay Systems

The article proposes a state control design approach for positive time-delay nonlinear systems in the presence of Lipschitz nonlinearities and parametric uncertainties. Using Lyapunov-Krasovskii theorem, conditions for asymptotic stability and the state-feedback control are formulated using expanded set of linear matrix inequalities, accounting time delays, system uncertainties and structural constraints. The advantage is a simple design procedure and closed-loop nonnegativity. A numerical example is presented to justify the proficiency and performance of the suggested technique.