Stabilization of stochastic nonlinear systems with multiplicative state sensing noise

Abstract In this paper, we study the stabilization problem of stochastic nonlinear systems with multiplicative state noise. A key obstacle arises when sensor faults are contaminated by multiplicative white noise, rendering the measured values inherently nondifferentiable across various points. This significantly compounds the complexity of designing effective output feedback control. To address this, we propose a novel design approach for stochastic nonlinear systems, aiming to identify a series of control gains. Recognizing the limitations of the classical quadratic Lyapunov function in handling the stochastic terms of the system, we choose to employ a series of quartic Lyapunov functions for discussion. Utilizing the selected series of control gains, we achieve the mean‐square stability for the closed‐loop system and ensure the convergence of the control to zero under expectation. Finally, the effectiveness of the designed series of control gains is verified through numerical simulations of a Newtonian system and a robotic manipulator system driven by a permanent magnet DC motor.