Homogeneous polynomially parameter-dependent state feedback controllers for finite time stabilization of linear time-varying systems

2013 ◽  
Author(s):  
Renato A. Borges ◽  
Joao Y. Ishihara ◽  
Hugo T. M. Kussaba ◽  
Larissa P. Silva
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Linear Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Time Varying Systems ◽  
Finite Time Stabilization ◽  
Parameter Dependent ◽  
Dependent State

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.

Finite-time dynamic output feedback stabilization of linear time-varying systems by a piecewise constant method

2018 ◽  
Vol 40 (14) ◽  
pp. 4078-4088
Author(s):  
Chao Liang ◽  
Chenxiao Cai ◽  
Jing Xu
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Linear Time ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Piecewise Constant ◽  
Output Feedback Controller ◽  
Dynamic Output ◽  
Time Varying Systems ◽  
Dynamic Output Feedback Controller

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

On the Design of Finite Time Settling Control for Linear Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 359-368 ◽  
Author(s):  
S. Choura
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Finite Time ◽  
Linear Time ◽  
Minimum Energy ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Final State ◽  
Variable Function ◽  
Time Varying Systems

The design of controllers combining feedback and feedforward for the finite time settling control of linear systems, including linear time-varying systems, is considered. The feedforward part transfers the initial state of a linear system to a desired final state in finite time, and the feedback part reduces the effects of uncertainties and disturbances on the system performance. Two methods for determining the feedforward part, without requiring the knowledge of the explicit state solutions, are proposed. In the first method, a numerical procedure for approximating combined controls that drive linear time-varying systems to their final state in finite time is given. The feedforward part is a variable function of time and is selected based on a set of necessary conditions, such as magnitude constraints. In the second method, an analytical procedure for constructing combined controls for linear time-invariant systems is presented, where the feedforward part is accurately determined and it is of the minimum energy control type. It is shown that both methods facilitate the design of the feedforward part of combined controllers for the finite time settling of linear systems. The robustness of driving a linear system to its desired state in finite time is analyzed for three types of uncertainties. The robustness analysis suggests a modification of the feedforward control law to assure the robustness of the control strategy to parameter uncertainties for arbitrary final times.

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