Trade Off Analysis Between Fixed‐Time Stabilization and Energy Consumption of Nonlinear Stochastic Systems

ABSTRACT The trade off analysis between the fixed‐time stabilization in probability and energy consumption of nonlinear stochastic system is studied in this paper. By constructing a switching controller and using inequality techniques, sufficient conditions for fixed‐time stabilization in probability in the Lyapunov sense are given, and the upper bounds of the settling time function and energy consumption are estimated. Then, by analyzing the relationship between control parameters, control time and energy consumption, the existence of trade off between control time and energy consumption is proposed, and the corresponding optimal parameter values are given. Finally, a numerical example is used to verify the validity of the theoretical results.