Reduced-order observer, homogeneous domination and nonsmooth output feedback stabilization of nonlinear systems

This paper focuses on the problem of adaptive output feedback stabilization for random nonlinear systems with unmodeled dynamics and uncertain nonlinear functions driven by colored noise. Under the assumption of unmodeled dynamics having enough stability margin, an adaptive output feedback stabilization controller is designed based on a reduced-order observer such that the state of the closed-loop system has an asymptotic gain in the 2-th moment (AG-2-M) and the mean square of the output can be made arbitrarily small by tuning parameters. A simulation example is used to illustrate the effectiveness of the control scheme.

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Global Output Feedback Stabilization of Nonlinear Systems with a Time-Varying Power and Unknown Output Function

Mathematical Problems in Engineering ◽

10.1155/2018/2906469 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12

Author(s):

Chao Guo ◽

Kemei Zhang

Keyword(s):

Nonlinear Systems ◽

Output Feedback ◽

Feedback Stabilization ◽

Time Varying ◽

Output Function ◽

Adding A Power Integrator ◽

Output Feedback Stabilization ◽

Open Sector ◽

Continuous Output ◽

Reduced Order Observer

This paper studies the problem of global output feedback stabilization for a class of nonlinear systems with a time-varying power and unknown output function. For nonlinear systems with a time-varying power and unknown continuous output function, by constructing a new nonlinear reduced-order observer together with adding a power integrator method, a new function to determine the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, it is shown that the equilibrium point of the closed-loop system can be guaranteed globally uniformly asymptotically stable by an output feedback controller.

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Further results on output-feedback stabilization of stochastic upper-triangular systems with state and input time-delays

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217705947 ◽

2017 ◽

Vol 40 (7) ◽

pp. 2408-2415 ◽

Cited By ~ 2

Author(s):

Liang Liu ◽

Shengyuan Xu ◽

Xuejun Xie ◽

Bing Xiao

Keyword(s):

Output Feedback ◽

Time Delays ◽

Delay System ◽

Feedback Stabilization ◽

System Stability ◽

Output Feedback Stabilization ◽

Triangular Systems ◽

Reduced Order Observer ◽

Input Time ◽

Stochastic Time

Based on stochastic time-delay system stability criterion and a homogeneous domination approach, the output-feedback stabilization problem for a class of more general stochastic upper-triangular systems with state and input time-delays has been solved in this paper. Firstly, the initial system is changed into an equivalent one with a designed scalar by introducing a set of coordinate transformations. After that, by designing an implementable homogeneous reduced-order observer, and tactfully selecting a suitable Lyapunov–Krasoviskii functional and a low gain scale, a delay-independent output-feedback controller is explicitly constructed. Finally, the globally asymptotically stability in probability of the closed-loop system is ensured by rigorous proof. The simulation results demonstrate the efficiency of the proposed design scheme.

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