Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics

A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system

“…(ii) It is still unclear what will happen when the controller is generated by an actuator with limited dynamics, an instance is the control switch in tracking sign changes. (iii) Some results on asymptotic stabilization and finitetime stabilization have been achieved for stochastic systems (Li, Xie, & Zhang, 2011;Shi, Yin, & Liu, 2013;Shi, Zhang, & Agarwal, 2015;Wu, Xie, Shi, & Xia, 2009;Wu, Xie, & Zhang, 2007;Xie, Duan, & Yu, 2011;Xie & Tian, 2009;Yu, Xie, & Duan, 2010), however, whether adaptive finitetime stabilization can be solved remains to be answered. …”

Reduced-order observer-based output feedback regulation for a class of nonlinear systems with iISS inverse dynamics

“…Yu et al and give the design of output feedback controller based on a reduced-order observer for a more general class of nonlinear systems with iISS inverse dynamics. Similarly, how to construct a counter-example to study the necessity of conditions on changing stochastic iISS supply rates in Yu, Xie, and Duan (2010) is an interesting future issue. Furthermore, the design method of output feedback controller based on a reduced-order observer in this article can be applied to and Yu, Xie, and Wu (2010).…”

Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates

“…Feedback interconnections were tackled in such a framework for stochastic nonlinear systems (Ito & Nishimura, in press-a;Wu, Karimi, & Shi, 2013;Wu, Xie, & ✩ 2 iISS generalizes ISS in the sense that a system is ISS only if it is iISS (Sontag, 1998). Zhang, 2007;Yu, Xie, & Duan, 2010). Importantly, for deterministic systems, it is known that compared with feedback interconnections, stability and robustness of cascaded systems can be established under milder conditions (Arcak, Angeli, & Sontag, 2002;Chaillet & Angelli, 2008;Ito, 2010;Panteley & Loría, 1998Sontag & Teel, 1995).…”