Fuzzy Control of 2-D Semi-Markov Jump Nonlinear Systems Subject to Actuator Saturation and Its Application in Tube-in-Tube Heat Exchange

This paper investigates the control problem of two-dimensional nonlinear semi-Markov jump systems with saturation constraints in the Roesser model. To address the nonlinearity of the system, the Takagi–Sugeno fuzzy model is employed, and a less conservative approach in handling the mismatched double fuzzy summation inequality is adopted, which removes the introduction of additional decision variables. Moreover, a novel mode generation method is employed, ensuring that the system mode index depends only on the sum of variables in two directions. In this case, the mode ambiguity problem in traditional methods is solved effectively. Furthermore, considering that the control input of a real two-dimensional process is limited by the physical capabilities of the actuator, actuator saturation is incorporated into the controller design within the proposed fuzzy framework. Then, by introducing concepts from the switching system and based on fuzzy model methods and Lyapunov theory, an almost inevitable exponential stability condition for the two-dimensional semi-Markov jump fuzzy nonlinear systems is established. By solving the optimization problem under the established stability condition, the attraction region is estimated. Finally, the effectiveness of the designed controller is verified through a numerical example and an example of heat exchange between a heated fluid inside a pipe.