Finite-time stabilization of linear systems by bounded linear time-varying feedback

Automatica ◽  
2020 ◽  
Vol 113 ◽  
pp. 108760 ◽  
Author(s):  
Bin Zhou
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Linear Time ◽  
Time Varying ◽  
Bounded Linear ◽  
Finite Time Stabilization

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.

Finite-Time Stabilization for Singular Linear Time-Delay Systems with Time-Varying Exogenous Disturbance

2012 ◽  
Vol 490-495 ◽  
pp. 2459-2463 ◽  
Author(s):  
Min Su ◽  
Shu Wei Wang ◽  
Xian Zhang
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Linear Time ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Delay Systems ◽  
Exogenous Disturbance ◽  
Exogenous Disturbances ◽  
Finite Time Stabilization

In this paper finite-time stabilization for singular linear time-delay systems with time-varying exogenous disturbances is defined. By combining Lyapunov approach and matrix inequality technique, a sufficient condition of the finite-time stabilization for this kind of systems is presented by a set of feasible problems involving linear matrix inequalities (LMIs) with nonlinear constraints. In addition, the nonlinear feasible problems are solved by an so-called cone complementary linearization (CCL) algorithm. The effectiveness of the approach proposed in this paper is presented by a numerical example.

scholarly journals Finite-Time Stabilization of Uncertain Switched Positive Linear Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Tianjian Yu ◽  
Yanke Zhong ◽  
Tefang Chen ◽  
Chunyang Chen
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Positive System ◽  
Time Varying ◽  
Polytopic Uncertainties ◽  
Finite Time Stabilization ◽  
Finite Time Boundedness ◽  
Definition Of

This paper is concerned with finite-time stabilization (FTS) analysis for a class of uncertain switched positive linear systems with time-varying delays. First, a new definition of finite-time boundedness (FTB) is introduced for switched positive system. This definition can simplify FTS analysis. Taking interval and polytopic uncertainties into account, a robust state feedback controller is built such that the switched positive linear system is finite-time bounded. Finally, an example is employed to illustrate the validities of obtained results.

Finite-Time Stabilization of Linear Time-Varying Continuous Systems

2009 ◽  
Vol 54 (2) ◽  
pp. 364-369 ◽  
Author(s):  
Germain Garcia ◽  
Sophie Tarbouriech ◽  
Jacques Bernussou
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Continuous Systems ◽  
Time Varying ◽  
Finite Time Stabilization
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