This paper considers an adaptive event‐triggered robust H∞ control for the Takagi–Sugeno (T‐S) fuzzy under the networked Markov jump systems (NMJSs) with time‐varying delay. First, a new adaptive event‐triggered scheme is developed to guarantee the T‐S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state‐feedback controller (mode‐dependent) in a closed‐loop form for stochastic stability for all admissible parameter uncertainties with an H∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck‐trailer application is used to demonstrate the effectively of the proposed algorithms.
Multiple model methods for nonlinear dynamical system control are appealing because local models can be simple and obvious, and global dynamics can be studied in terms of transitions between small operating zones. In this study, we propose that using qualitative models strengthens the multiple model method even more by enabling each local model to explain a huge class of effective nonlinear dynamical systems. Furthermore, reasoning using qualitative models reveals weak necessary conditions sufficient to verify qualitative features like stability analysis. The authors show the method by creating a global controller for the free pendulum. In addition, local controllers are specified and validated by comparing their patterns to basic general qualitative models. Our proposed procedure establishes qualitative limitations on controller designs that are sufficient to ensure the necessary local attributes and to establish feasible transitions between local areas for the existing problems. As a result, the continuous phase picture may be reduced to a simple transitional graph. The degrees of freedom in the system that are not bound by the qualitative description are still accessible to the designer for optimization for any other purpose. An example of a pendulum plant illustrates the effectiveness of the proposed method.
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