Stability analysis of random nonlinear systems with time-varying delay and its application

This paper studies a class of random nonlinear systems with time-varying delay, in which the r-order moment of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time-delay systems. Secondly, some criteria on noise-to-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, an adaptive output feedback regulation controller is constructed for a class of random nonlinear time-delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example. (C) 2020 Elsevier Ltd. All rights reserved.