Dynamic State Feedback Stabilization of Stochastic Cascade Nonlinear Time-Delay Systems With SISS Inverse Dynamics

• Published in: IEEE transactions on automatic control Vol. 64; no. 12; pp. 5132 - 5139
• Main Authors: Xie, Xue-Jun, Jiang, Mengmeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Asymptotical stabilization; Closed loop systems; Control design; Dynamic stability; Feedback control; Inverse dynamics; Nonlinear dynamical systems; Nonlinear systems; Stability criteria; State feedback; stochastic cascade nonlinear time-delay systems; stochastic input-to-state stability (SISS) inverse dynamics; Time delay systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2910166

This paper investigates state feedback stabilization problem of a class of stochastic cascade nonlinear time-delay systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with stochastic input-to-state stability condition, without imposing any growth condition on time-delay system nonlinearities, a delay-independent, dynamic state feedback controller is constructed. It is shown that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability.