Abstract
In this paper, we deal with a class of neutral random nonlinear systems. The existence and uniqueness of the solution to neutral random functional nonlinear systems (NRFSs) are established. Furthermore, the criteria on noise-to-state stability in the moment of a special class of NRFSs, named neutral random delay nonlinear systems, are derived. An example is given for illustration.
Highlights
Stochastic differential equations (SDEs) are widely adopted to describe systems with stochastic disturbances
Taking the environmental disturbances into account, Kolmanovskii and Nosov [8] and Mao [9] discussed the neutral stochastic differential equations with delay driven by Brownian motion (NSDDEs)
Many efforts have been made on this topic, especially on asymptotical boundedness and exponential stability of NSDDEs
Summary
Stochastic differential equations (SDEs) are widely adopted to describe systems with stochastic disturbances. In Wu [14], a framework of stability analysis for random nonlinear systems with second-order processes was established. Based on the above works, Zhang et al [18] investigated the noise-to-state stability in probability of state-dependent switched random nonlinear systems with second-order stationary processes. Zhang et al [15] and Zhang et al [19] established the criteria on noise-tostate stability in the moment of random switched systems under a reasonable assumption of second-order processes, respectively. 4, the criteria of noise-to-state exponential stability in the pth moment of neutral random delay nonlinear systems are established. Theorem 1 Under Assumptions A1–A4, the neutral random functional nonlinear system (2) has a unique solution.
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