Achieving vector relative degree for nonlinear systems with parametric uncertainties

1995 ◽  
Vol 5 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Carla A. Schwartz ◽  
Peter W. Gibbens ◽  
Minyue Fu
Keyword(s):  
Nonlinear Systems ◽  
Relative Degree ◽  
Parametric Uncertainties

Funnel control for nonlinear systems with higher relative degree

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Thomas Berger ◽  
Huy Hoàng Lê ◽  
Timo Reis
Keyword(s):  
Nonlinear Systems ◽  
Relative Degree ◽  
Funnel Control

scholarly journals Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Meng-Meng Jiang ◽  
Xue-Jun Xie
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Parametric Uncertainties ◽  
Nonlinear Functions ◽  
Sign Function ◽  
Dynamic Uncertainty ◽  
Finite Time Stabilization

Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.

scholarly journals Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhongwei Lin ◽  
Jizhen Liu ◽  
Yuguang Niu
Keyword(s):  
Nonlinear Systems ◽  
Control Design ◽  
Relative Degree ◽  
Backstepping Technique ◽  
Markovian Jump ◽  
Design Problems ◽  
Stabilizing Control ◽  
Full State ◽  
Degree Set ◽  
Coordinate Changes

This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree setn,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.

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