This paper aims to solve the state feedback stabilization problem for a class of high-order nonlinear systems with more general high-order terms. Based on the backstepping design method and Lyapunov stability theorem, a state feedback controller is constructed to ensure that the origin of the closed-loop system is globally asymptotically stable. The efficiency of the state feedback controller is demonstrated by a simulation example.
AndrieuVPralyLAstolfiA (2008) Homogeneous approximation, recursive observer and output feedback. SIAM Journal on Control and Optimization47: 1814–1850.
2.
ChenWSWuJJiaoLC (2012) State-feedback stabilization for a class of stochastic time-delay nonlinear systems. International Journal of Robust and Nonlinear Control22: 1921–1937.
3.
FuJMaRCChaiTY (2015) Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica54: 360–373.
4.
HaleJ (1980) Ordinary Differential Equations. New York: John Wiley & Sons.
5.
KartsatosAG (2005) Advanced Ordinary Differential Equations. New York: Hindawi.
LiWQLiuLFengG (2017) Cooperative control of multiple stochastic high-order nonlinear systems. Automatica82: 218–225.
10.
LiWQLiuLFengG (2018) Output tracking of stochastic nonlinear systems with unstable linearization. International Journal of Robust and Nonlinear Control28: 466–477.
11.
LiJQianCJ (2006) Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems. IEEE Transactions on Automatic Control51: 879–884.
12.
LiWQXieXJZhangSY (2011) Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions. SIAM Journal on Control and Optimization49: 1262–1282.
13.
LiWQXieLHZhangJF (2015) Containment control of leader-following multi-agent systems with Markovian switching network topologies and measurement noises. Automatica51: 263–267.
14.
LiWQZhangJF (2014) Distributed practical output tracking of high-order stochastic multi-agent systems with inherent nonlinear drift and diffusion terms. Automatica50: 3231–3238.
15.
LinW (2000) Adding one power integrator: A tool for global stabilization of high order lower-triangular systems. Systems and Control Letters39: 339–351.
16.
LiuLDuanN (2010) State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power. Nonlinear Analysis: Modelling and Control15: 39–53.
17.
LiuLYangXB (2017) Robust adaptive state constraint control for uncertain switched high-order nonlinear systems. IEEE Transactions on Industrial Electronics64: 8108–8117.
18.
LiuLYinSGaoHJet al. (2015) Adaptive partial-state feedback control for stochastic high-order nonlinear systems with stochastic input-to-state stable inverse dynamics.Automatica51: 285–291.
19.
LiuYG (2014) Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems. SIAM Journal on Control and Optimization52: 1886–1913.
20.
PolendoJQianCJ (2007) A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback. International Journal of Robust and Nonlinear Control17: 605–629.
21.
PolyakovA (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control57: 2106–2110.
22.
QianCJLinW (2000) Almost disturbance decoupling for a class of high-order nonlinear systems. IEEE Transactions on Automatic Control45: 1209–1214.
23.
QianCJLinW (2001a) A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control46: 1061–1079.
24.
QianCJLinW (2001b) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Systems and Control Letters42: 185–200.
25.
QianCJLinW (2006) Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems. IEEE Transactions on Automatic Control51: 1457–1471.
26.
SongZBYangSHSunZYet al. (2016) Global stabilization via nested saturation function for high-order feedforward nonlinear systems with unknown time-varying delays. International Journal of Robust and Nonlinear Control26: 3363–3387.
27.
SunZYLiTYangSH (2016) A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems. Automatica70: 249–257.
28.
SunZYLiuYG (2007) Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica43: 1772–1783.
29.
SunZYLiuYGZhangXH (2015a) New results on global stabilization for time-delay nonlinear systems with low-order and high-order growth conditions. International Journal of Robust and Nonlinear Control25: 878–899.
30.
SunZYXueLRZhangKM (2015b) A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system. Automatica58: 60–66.
31.
SunZYYangSHLiT (2017a) Global adaptive stabilization for high-order uncertain time-varying nonlinear systems with time-delays. International Journal of Robust and Nonlinear Control27: 2198–2217.
32.
SunZYYunMMLiT (2017b) A new approach to fast global finite-time stabilization of high-order nonlinear systems. Automatica81: 455–463.
TianWSZhangCLLiSH (2014) Global stabilization of inherently non-linear systems using continuously differentiable controllers. Nonlinear Dynamics77: 739–752.
35.
WangTCLiWQ (2016) State-feedback stabilization of stochastic nonlinear systems with time-varying delay and different orders. Asian Journal of Control18: 1159–1164.
36.
XieXJLiuL (2013) A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay. IEEE Transactions on Automatic Control58: 494–499.
37.
ZhangXHZhangKMXieXJ (2016) Finite-time output feedback stabilization of nonlinear high-order feedforward systems. International Journal of Robust and Nonlinear Control26: 1794–1814.