Exponential stability and stabilization of positive T‐S fuzzy delayed systems

Abstract

The analysis of positive nonlinear delayed systems is of great importance for many real‐world applications. Such systems' stability and stabilization assessment is still an open topic, and there is limited literature on this field. Moreover, further convergence conditions should be considered for many experimental processes, such as exponential stability analysis, which is highly important. Considering the above, we deal in this study with the problem of exponential stability and stabilization of nonlinear fuzzy positive systems with delay. We establish exponential stability criteria using Lyapunov–Krasovskii functional (LKF) and a delay bi‐decomposition approach for bounded and time‐varying delayed systems. The obtained results are then extended to the exponential stabilization case. The control law is designed using Parallel distributed compensation (PDC). The proposed approach, formulated in terms of linear matrix inequalities (LMIs), allows reducing the conservativeness of the delay‐dependent conditions. A comparative study is presented to illustrate the superiority of our method. Moreover, simulation results for the two tanks process show the advantages of the proposed control design.