Reliable Quantized Fuzzy Controller Design for Nonlinear Singularly Perturbed Systems With Markovian Jumps and Dynamic Event Triggered Mechanism

Abstract

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.

Keywords

• Markov jump singularly perturbed systems
• CBDETM
• quantization
• reliable control