Quantum mechanics

Adaptive control

Algorithm

Control (management)

Step response

Engineering

Pure mathematics

Backstepping

Biology

Bandwidth (computing)

Control engineering

Full state feedback

Stability (learning theory)

Computer science

Controller (irrigation)

Settling time

Computer network

Physics

Nonlinear system

Corollary

Upper and lower bounds

Mathematics

Agronomy

Lyapunov function

Mathematical analysis

Artificial intelligence

Control theory (sociology)

Lyapunov stability

Integrator

Machine learning

State (computer science)

IEEE/CAA Journal of Automatica Sinica

This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems. We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure. In particular, an important corollary is obtained, which can give a less conservative upper-bound estimate of the settling time. Based on the backstepping technique and the addition of a power integrator method, a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems. It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria. Finally, the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.

Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems