A Combined Homogeneous Domination and Sign Function Approach to Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems

Further results on global state feedback stabilization of high-order nonlinear systems with time-varying delays

“…[20]). For x A R, y A R, p Z 1 and c 4 0 are constants, the following inequalities hold: (i) jx þ yj p r 2 p À 1 jx p þ y p j, (ii) ðjxjþjyjÞ 1=p r jxj 1=p þjyj 1=p r 2 ðp À 1Þ=p ðjxjþjyjÞ 1=p , (iii) jjxjÀjyjj p r jjxj p Àjyj p j, (iv) jxj p þjyj p r ðjxjþjyjÞ p , (v) j½x 1=p À½y 1=p j r 2 1 À 1=p jx À yj 1=p , (vi) j½x p À½y p j r cjx À y J jx À yj p À 1 þjyj p À 1 j. Lemma 2.2 (Yang and Lin [21]).…”

“…(1) under Assumption 2.1, the continuous state feedback controller (20), which preserves the equilibrium at the origin, renders that the closedloop system state globally asymptotically converges to zero.…”

“…If Assumption 2.1 holds when r n þ τ Z max 1 r i r n fr i g, then the system (1) can be globally asymptotically stabilized by continuously differentiable state feedback controller (20).…”

Global Output Feedback Stabilization for a Class of Nonlinear Cascade Systems

“…Since some nonlinear functions satisfy neither the linear growth nor Lipschitz condition in practice, the existing approaches are not suitable. Therefore, [16][17][18][19] proposed homogeneous domination method to overcome this obstacle. Based on the existing results, some special observers are proposed, such as dualobserver [20] and reduced-observer [21].…”

Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone

“…The systems subject to the stochastic disturbance are usually termed as stochastic systems that have also been widely probed, with switching dynamics (Hou, Fu, & Duan, 2013;Wu, Cui, Shi, & Karimi, 2013;Wu, Yang, & Shi, 2010;Wu, Zheng, & Gao, 2013;Zhang, Wu, & Xia, 2014) or without (Wu, Xie, & Zhang, 2007;Xie & Duan, 2010;Xie, Duan, & Yu, 2011;Xie, Duan, & Zhao, 2014;Xie & Liu, 2012). To mention a few, the dissipativity-based sliding mode control was adopted in Wu, Zheng et al (2013) for switched stochastic linear systems.…”