Multirate-Sampled Fuzzy Consensus Control for Nonlinear Markov-Switched MASs With Time-Varying Delays: An Ellipsoidal Attraction-Region-Constrained Method

This study investigates the mean-square reachable set (RS) consensus of nonlinear Markov-switched multiagent systems (MASs) with time-varying delays, in which a multirate sampled-data consensus (MRSDC) control scheme is designed for the first time under general uncertain semi-Markov transition (GUST) switched topologies. First, the nonlinear Markov-switched MAS is transformed into quasilinear subsystems by applying the Takagi-Sugeno (T-S) fuzzy modeling technique, where the GUST-based Markov model characterizes both the operation mode and abrupt variations in the communication network topologies among all agents. Second, an aperiodic MRSDC control strategy is developed to reduce the sampling frequency of certain sensors below the single-rate threshold by adaptively adjusting their sampling rates, thereby enhancing flexibility and improving consensus performance. Furthermore, a new free-weighting integral inequality is introduced to handle the integral quadratic term involving time-varying delay bounds. Subsequently, an appropriate looped-side Lyapunov functional is designed, leveraging aperiodic multirate sampling and time-varying delay characteristics. Next, by combining the constructed Lyapunov functional with the proposed integral inequality and an improved reciprocally convex combination inequality, sufficient conditions are derived in the form of linear matrix inequalities (LMIs). These conditions not only ensure the mean-square leaderless consensus of the resulting MASs but also guarantee that all reachable states remain confined within ellipsoidal attracting-like regions under the MRSDC scheme. Finally, numerical validations are conducted to demonstrate the effectiveness of the proposed MRSDC control strategies using interconnected single-link robot arm systems (SLRASs), while a comparative numerical example further illustrates the superiority of the proposed method.