Dissipative control for T–S fuzzy descriptor systems with actuator saturation and disturbances

Abstract

In this paper, dissipative control methods are proposed for a type of nonlinear descriptor system via T–S fuzzy model with actuator saturation and L2-disturbances. The admissible conditions are first derived such that the system is not only regular, impulse-free but also bounded state stable. The disturbance tolerance capability is assessed and the corresponding problems are expressed as Linear matrix inequality (LMI) optimization problems. Then, in order to measure the disturbance rejection capability of the system, an H∞ fuzzy controller and a dissipative controller are designed based on the admissible condition such that the closed-loop system is regular, impulse-free, bounded state stable and holds the H∞ performance or dissipative performance. The obtained method eliminates impulse phenomena due to the characteristics of a descriptor system, and hence guarantees the existence and uniqueness of solutions. Finally, by using the feasp solver and min cx solver from the LMI toolbox, simulations are performed to validate the presented methods for a class of nonlinear biological economy systems described by T–S fuzzy descriptor models. The results indicate that the designed method can eliminate the impulse phenomena at the bifurcation value, stabilize the closed-loop system in bounded state and achieve H∞ performance and dissipative performance in occurrence of actuator saturation. This ensures the ecological balance of the economy system with actuator saturation and L2-disturbance for juvenile populations.