Observer-based control of positive polynomial fuzzy systems with unknown time delay
Abstract This paper presents a methodology to investigate the observer-based control for positive nonlinear systems with unknown time delay through analyzing the stability and positivity of positive polynomial fuzzy-model-based (PPFMB) observer-control systems with unknown time delay and unmeasurable premise variables. In order to widen the application of research results and relax the research results, the polynomial fuzzy observer-controller employs a membership function depending on estimated premise variables and the observer system matrix is treated as decision variable. This scenario will lead to non-convex stability and positivity conditions when the stability and positivity are analyzed based on the Lyapunov stability theory. To overcome this issue, some transformation techniques and matrix decoupling techniques (MDT) are adopted to turn the non-convex stability/positivity conditions into convex ones so that they can be handled by convex programming techniques. Finally, two simulation examples are presented to demonstrate the feasibility and validity of the analysis results.