scholarly journals State-Feedback Stabilization for Stochastic High-Order Nonlinear Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fangzheng Gao ◽  
Zheng Yuan ◽  
Fushun Yuan
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Design Procedure ◽  
High Order ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Nonlinear Growth ◽  
Adding A Power Integrator ◽  
Power Integrator ◽  
Weaker Conditions

This paper investigates the problem of state-feedback stabilization for a class of stochastic high-order nonlinear systems with time-varying delays. Under the weaker conditions on the power order and the nonlinear growth, by using the method of adding a power integrator, a state-feedback controller is successfully designed, and the global asymptotic stability in the probability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov-Krasovskii functional. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

scholarly journals State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power

2010 ◽  
Vol 15 (1) ◽  
pp. 39-53 ◽  
Author(s):  
L. Liu ◽  
N. Duan
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Optimal Stabilization ◽  
Adding A Power Integrator ◽  
Power Integrator ◽  
Smooth State

This paper investigates the problem of globally asymptotically stable in probability by state-feedback for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique and choosing an appropriate Lyapunov function, a linear smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability. Furthermore, we address the problem of state-feedback inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the proposed approach.

Asymptotic stabilization of stochastic high-order upper-triangular nonlinear systems with input time-varying delay

2016 ◽  
Vol 39 (12) ◽  
pp. 1898-1905 ◽  
Author(s):  
Liang Liu ◽  
Yifan Zhang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Feedback Stabilization ◽  
System Stability ◽  
Time Varying ◽  
Independent State ◽  
Time Varying Delay ◽  
Input Time ◽  
Varying Delay

Based on the homogeneous domination approach and stochastic nonlinear time-delay system stability criterion, this paper investigates the global state-feedback stabilization problem for a class of stochastic high-order upper-triangular nonlinear systems with input time-varying delay. By skilfully choosing an appropriate Lyapunov–Krasoviskii functional and successfully solving several troublesome obstacles in the design and analysis procedure, a delay-independent state-feedback controller is designed to render the closed-loop system globally asymptotically stable in probability. The simulation example is given to verify the effectiveness of the proposed design scheme.

A State-scaling Design for Prescribed-time Stabilization of High-order Nonlinear Systems with Input Quantization

2021 ◽  
Author(s):  
Wenhui Zhang ◽  
Fangzheng Gao ◽  
Jiacai Huang ◽  
Yuqiang Wu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Equivalent Transformation ◽  
Input Quantization ◽  
Adding A Power Integrator ◽  
Performance Requirements ◽  
System States ◽  
Power Integrator ◽  
New Framework

Abstract This article considers global stabilization problem for a kind of uncertain high-order nonlinear systems (HONSs). Two distinct characteristics of this study are that the considered system possesses the input-quantized actuator, and the prescribed time convergence of the system states is wanted. To address these, a novel state-scaling transformation (SST) is firstly introduced to convert the aboriginal prescribed-time stabilization (PTS) to the asymptotic stabilization of the transformed one. Then, under the new framework of equivalent transformation, a quantized state feedback controller that achieves of the performance requirements is developed with the aid of the technique of adding a power integrator (API). Finally, simulation results of a liquid-level system are provided to confirm the efficacy of the proposed approach.

scholarly journals Global Finite-Time Stabilization for a Class of Uncertain High-Order Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jian Wang ◽  
Jing Xie ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Finite Time Stability ◽  
Adding A Power Integrator ◽  
System A ◽  
Continuous State ◽  
Finite Time Stabilization ◽  
Power Integrator

This paper addresses the problem of global finite-time stabilization by state feedback for a class of high-order nonlinear systems under weaker condition. By using the methods of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee the global finite-time stability of the resulting closed-loop system. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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