Stability analysis and constrained control of a class of fuzzy positive systems with delays using linear copositive Lyapunov functional

This paper deals with the stability of nonlinear continuous-time positive systems with delays represented by the Takagi-Sugeno (T-S) fuzzy model. A simpler sufficient condition of stability based on linear copositive Lyapunov functional (LCLF) is derived which is not relevant to the magnitude of delays. Based on the result of stability, the problem of controller design via the so-called parallel distributed compensation (PDC) scheme is solved. The control is under a positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained positive control is also considered, further requiring that the trajectory of the closed-loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results are formulated as linear programs (LPs) and linear matrix inequalities (LMIs), and the control laws can be obtained by solving a set of bilinear matrix inequalities (BMIs). A numerical example and a real plant are studied to demonstrate the efficiency of the proposed method. © Springer Science+Business Media, LLC 2012.