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This paper proposes a novel approach to handling random actuator failures in control systems through robust and reliable control techniques. The investigation seeks to establish a framework for assessing the $ l_{2}-l_{\infty } $ stability characteristics of nonlinear Markov jump singularly perturbed systems (MJSPSs) using an output Takagi-Sugeno (TS) fuzzy-based controller. The study focuses on implementing a component-based dynamic event-triggered mechanism (CBDETM), including quantization, to investigate the transmission of the outputs across networked communication channels. The proposed approach is based on the following key attributes: 1) An event-triggered mechanism that establishes a suitable condition for independent signal transmission from each sensor node to the controller; 2) A stochastic failure model that describes actuator failures; 3) A non-stationary Markov chain that reflects the asynchronous relationship between the system and controller modes; 4) A mode-dependent Lyapunov function is used to establish sufficient conditions to show that the resultant closed-loop system is stochastically mean-square stable with a $\gamma $ level of $ l_{2}-l_{\infty } $ performance index; 5) The theoretical findings are validated by a real numerical example of the Van Der Pol circuit, confirming the effectiveness of the proposed strategy.

We present a new family of ninth‐order hybrid explicit Numerov‐type methods, effectively utilizing only eight stages, for solving the special second‐order initial value problem. After applying a number of simplifying assumptions, we arrive to a reduced set of order conditions. Then, we derive an optimal method with constant coefficients that requires one less stage than standard methods found in the literature that use nine stages at this moment. Numerical tests are conducted using quadruple precision arithmetic on several well‐known problems and the superiority of the new method is clear. Finally, in Section 6, a Mathematica package is presented that implements the corresponding algorithm. [ABSTRACT FROM AUTHOR]