On Input Delay Tolerance of Stochastic Nonlinear Systems with Dominant Homogeneity of Degree Zero

This paper investigates the problem of when stochastic nonlinear systems that are $l$ th moment asymptotically stabilizable ( $l$ th MAS) are tolerant to input delay. Our focus is on, substantially different from the existing works in the literature, a class of stochastic systems that may be neither locally Lipschitz continuous (LLC) nor linear growth, and not $l$ th MAS by smooth feedback. To address the problem of input delay tolerance (IDT), we first present the existence of the solutions for a class of continuous stochastic time-delay systems and establish almost sure forward completeness under appropriate homogeneity conditions. Using the theory of stochastic homogeneous systems, we then prove that for stochastic nonlinear systems with dominant homogeneity of degree zero, $l$ th moment asymptotic stabilizability by homogeneous feedback is preserved in the presence of limited input delay. As a consequence, new results are obtained on the IDT for certain stochastic nonlinear systems with input delay such as lower-triangular, upper-triangular, and non-triangular systems with inherent nonlinearity.