A delayed Takagi–Sugeno fuzzy control approach with uncertain measurements using an extended sliding mode observer

In this study, a sliding mode observer (SMO) is implemented on a T–S fuzzy system with multiple time–varying delays over continuous time. Because state data may not be fully available in practice, state observers are used to estimate state information. A system based on observers is implemented with non–parallel distribution compensation (N-PDC). Moreover, the concept of dissipative control provides a framework for analyzing the performance of H_∞, L₂−L_∞, and dissipativeness. In order to design two sliding surfaces using the SMO gain matrix, first two integral–type sliding surfaces must be constructed. Then, we define a few additional parameters using fuzzy Lyapunov stability and SMO theory, resulting in asymptotically stable closed–loop performances. On the basis of the new error system, convex optimization is used to generate the sliding mode controller and the gained weight matrices. Following is an example of the power system (ship electric propulsion) to demonstrate the potential scheme.