Abstract
In real-world applications, faults and delays can occur in all system variables such as inputs and/or states and/or outputs. The challenge of designing Takagi-Sugeno (T–S) fuzzy controllers for faulty and fully delayed systems is addressed. In contrast to most existing works, the system states are assumed to be unavailable for measurement, and no prior information about the system delays and faults as well as their boundaries is required. Furthermore, the time delays are multiple, unknown, and different in each distinct input and/or state and/or output. Because the system states, delays, and faults are unavailable and unknown, the T–S fuzzy controller premise variables become immeasurable. Thus, the design of fuzzy state observers and fuzzy controllers under the presence of all previous uncertainties to ensure overall system stability has become a big challenge. This challenge is solved in two stages. First, a new model for a fully delayed system with different delays in each distinct input, and/or state, and/or output is obtained, which is realized by transforming the fully delayed system into a general delayed model with delayed states and inputs as well as the biasing uncertainties in the sensors. Subsequently, the T–S fuzzy-descriptor systems are investigated, and simultaneous fault-tolerant T–S fuzzy observers–controllers are proposed. The overall stabilities are ensured using the Lyapunov–Krasovskii functional method. Three simulated examples are presented to prove the applicability and advantages of the proposed approach.