Fixed-Time Lyapunov Criteria of Stochastic Nonlinear Systems and Its Generalization
Huifang Min, Shang Shi, Shengyuan Xu, Jian Guo, Zhengqiang Zhang
Abstract
This study investigates the fixed-time stability of stochastic nonlinear systems described by Itô differential equations. The improved fixed-time Lyapunov theorem is given and an important corollary is obtained. It is proved that the upper-bound estimate of the settling time is less conservative. We establish a new definition of practically fixed-time stability in probability and propose the corresponding Lyapunov criterion theorem. In addition, different cases of the parameters are discussed to provide a less conservative upper-bound estimate of the settling time. The effectiveness of the proposed stability and controller is demonstrated by two simulation examples.
Topics & Concepts
MathematicsUpper and lower boundsCorollarySettling timeLyapunov functionGeneralizationNonlinear systemApplied mathematicsLyapunov stabilityControl theory (sociology)Stability (learning theory)Lyapunov equationLyapunov redesignLyapunov exponentMathematical analysisComputer scienceControl (management)Discrete mathematicsEngineeringArtificial intelligenceControl engineeringQuantum mechanicsMachine learningPhysicsStep responseAdaptive Control of Nonlinear SystemsStability and Control of Uncertain SystemsGuidance and Control Systems