Delay-Dependent Admissibility Analysis and Dissipative Control for T-S Fuzzy Time-Delay Descriptor Systems Subject to Actuator Saturation

In this paper, a delay-dependent admissibility analysis method and dissipative controller design are developed for a class of nonlinear time-delay descriptor systems subject to actuator saturation and <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula>-disturbances via a Takagi-Sugeno (T-S) fuzzy model. A less conservative admissible condition is first derived under which the system is not only regular, impulse free but also stable under certain initial conditions. The method can eliminate the impulsive behavior of a descriptor system so as to ensure the existence and uniqueness of solutions. The estimate of attraction domain is also determined in which the admissible initial states converge asymptotically to the origin. The disturbance attenuation capability is studied by designing the dissipative fuzzy controller such that the closed-loop system is admissible and holds the dissipative performance for the prescribed disturbance attenuation level and <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula>-disturbances. The method is more suitable for admissibility analysis and robust control synthesis. Moreover, <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control processes can be achieved in the same design process, which shows that the cost and time may potentially be reduced when a controller is designed for an actual physical system. Simulations are performed to validate the proposed methods and illustrate the decrease in conservativeness for a classic nonlinear system based on the T-S fuzzy time-delay descriptor model under actuator saturation and <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula>-disturbances. The study seeks to establish a foundation for investigating the control synthesis of T-S fuzzy time-delay descriptor systems subject to actuator saturation.

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