Adaptive event‐triggered robust <i>H</i><sub><i>∞</i></sub> control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay
Muhammad Shamrooz Aslam, Irfan Qaisar, Abdul Majid, Summera Shamrooz
Abstract
Abstract 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.