Further results on adaptive state feedback stabilization for a class of stochastic feedforward nonlinear systems with time delays

2018 ◽  
Vol 41 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Xiaoyan Qin ◽  
Huifang Min
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Transformation Technique ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper further discusses the state feedback stabilization for stochastic high-order feedforward nonlinear systems with input time delay. By constructing the appropriate Lyapunov–Krasovskii functional, and using the variable transformation technique and the homogeneous domination idea, a state feedback controller is designed to ensure that the closed-loop system will be globally asymptotically stable in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.

scholarly journals State Feedback Control for Stochastic Feedforward Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Liang Liu ◽  
Ming Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Asymptotically Stable ◽  
Stabilization Problem ◽  
Closed Loop System ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems. By using the homogeneous domination approach, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. A simulation example is provided to show the effectiveness of the designed controller.

Semiglobal Output Feedback Stabilization of a Generalized Class of MIMO Nonlinear Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Junyong Zhai ◽  
Chunjian Qian ◽  
Hui Ye
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Output Feedback Stabilization ◽  
Mismatched Uncertainties ◽  
Semiglobal Stabilization

This paper considers the problem of semiglobal stabilization by output feedback for a class of generalized multi-input and multi-output uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. Combining the output feedback domination approach and block-backstepping scheme together, a series of linear output feedback controllers are constructed recursively for each subsystems and the closed-loop system is rendered semiglobally asymptotically stable.

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.

State feedback stabilization for nonlinear systems with more general high-order terms

2018 ◽  
Vol 41 (3) ◽  
pp. 615-620
Author(s):  
Tiancheng Wang ◽  
Shi Zheng ◽  
Wuquan Li
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Design Method ◽  
High Order ◽  
The State ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Closed Loop System ◽  
Globally Asymptotically Stable ◽  
State Feedback Controller

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.

An LMI Approach to State Feedback H∞ Control for Switched Singular Linear Systems

2014 ◽  
Vol 875-877 ◽  
pp. 835-840
Author(s):  
Zhu Mu Fu ◽  
Bin Wang ◽  
Ai Yun Gao
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lmi Approach ◽  
Singular Linear Systems

In this paper, the problems of state feedback control for a class of switched singular linear systems are investigated. By constructing a novel switched Lyapunov functional and convex combinations techniques, a sufficient condition established in terms of strict linear matrix inequalities (LMIs) is presented such that the system is asymptotically stable and satisfies performance. An explicit expression for the state feedback stabilization sub-controller and switching rule are designed. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, in which the closed-loop system satisfies performance at each point in whole state-space through switching, although each sub-system doesn’t satisfy the performance and even is not asymptotically stable. A numerical example is provided to illustrate the validity of the proposed methods.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

2018 ◽  
Vol 41 (7) ◽  
pp. 1888-1895
Author(s):  
Fangzheng Gao ◽  
Yanling Shang ◽  
Yuqiang Wu ◽  
Yanhong Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Dead Zone ◽  
Fixed Time ◽  
High Order ◽  
Closed Loop System ◽  
Sign Function ◽  
Input Nonlinearity ◽  
Power Integrator

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jinsheng Xing ◽  
Naizheng Shi
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Closed Loop ◽  
Loop System ◽  
Asymptotically Stable ◽  
Bilinear Model ◽  
Closed Loop System ◽  
Fuzzy Modelling ◽  
Control Scheme

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

Observer-Based Control of a Class of Switched Fuzzy Systems

2014 ◽  
Vol 945-949 ◽  
pp. 2539-2542
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Function Method ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lyapunov Function Method ◽  
Switching State

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

scholarly journals Asymptotic Stabilization by State Feedback for a Class of Stochastic Nonlinear Systems with Time-Varying Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Wang ◽  
Wuquan Li ◽  
Xiuhong Wang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Control Coefficients

This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.

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