Quantized control based on fixed-time and predefined-time stabilization of coupled Filippov systems on networks with mismatched parameters

This paper mainly investigates the fixed-time and predefined-time stabilization of coupled Filippov systems on networks with mismatched parameters, which is more general and realistic than the related ones. The indefinite function is adopted and more generalized inequality conditions on the Lyapunov function are provided. Based on the inequality techniques and comparison principle, some novel fixed-time and predefined-time stability lemmas are established. Detailed analysis shows that the estimations of settling-time based on different inequalities including basic inequality and Tchebycheff inequality are not equal. The relationships between the estimations of settling-time are also given. As for complex systems, quantized control can have advantages in terms of simplicity, robustness, and ease of implementation. By designing the quantized control strategies and based on the new proposed fixed-time and predefined-time stability lemmas, the fixed-time and predefined-time stabilization of the addressed networks are achieved, which lead to some new results on the complex networks. Finally, numerical simulations are given to verify the main results.