Fixed time stability of impulsive stochastic nonlinear time‐varying systems

Haiqi Peng, Quanxin Zhu

2023International Journal of Robust and Nonlinear Control25 citationsDOI Open Access PDF

Abstract

Abstract The aim of the article is to discuss stochastic fixed‐time (FIXT) stability of impulsive stochastic nonlinear time‐varying systems. By using the multiple Lyapunov method and stochastic analysis theory, several novel stability theorems for determining stochastic FIXT stability are established. Concurrently, the estimation of stochastic settling time is given. Compared with other conclusions about stochastic FIXT stability, the results can be more widely applied to impulsive stochastic nonlinear time‐varying systems, the constraint of the impulse strength factor and the differential operator are also relaxed. Furthermore, some corollaries are obtained to establish stochastic FIXT stability of impulsive stochastic nonlinear time‐varying systems.

Topics & Concepts

Nonlinear systemStability (learning theory)MathematicsControl theory (sociology)Impulse (physics)Lyapunov functionStochastic processSettling timeApplied mathematicsComputer scienceEngineeringPhysicsStatisticsControl engineeringQuantum mechanicsMachine learningArtificial intelligenceStep responseControl (management)Stability and Control of Uncertain SystemsAdaptive Control of Nonlinear SystemsFault Detection and Control Systems