Global stabilization of the discrete-time double integrator using a saturated linear state feedback controller

2011 ◽  
Author(s):  
Tao Yang ◽  
Anton A. Stoorvogel ◽  
Ali Saberi
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Feedback Controller ◽  
Global Stabilization ◽  
State Feedback Controller ◽  
Linear State ◽  
Double Integrator

Finite-Time Control for Switched Discrete-Time System

2013 ◽  
Vol 313-314 ◽  
pp. 516-523
Author(s):  
Wei Ming Xiang ◽  
Yong Chi Zhao
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Average Dwell Time ◽  
Feedback Controller ◽  
Time Interval ◽  
Discrete Time System ◽  
State Feedback Controller ◽  
Fast Switching ◽  
Slow Switching

Finite-time stability concerns the boundless of system during a fixed finite-time interval. In this paper, the problem of finite-time stabilization for switched discrete-time systems is addressed. Both the fast switching and slow switching case are considered. In fast switching case, the designed state feedback controller combines controllers for each subsystem and resetting controller at switching instant, it is shown that the resetting controller can reduce the conservativeness on controller design. Under slow switching, state feedback controller is designed with admissible average dwell time. Several numerical examples are given to illustrate the proposed results within this paper.

scholarly journals Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402092265
Author(s):  
Xiao Yu ◽  
Fucheng Liao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
State Feedback ◽  
Feedback Controller ◽  
Matrix Inequality ◽  
State Feedback Controller ◽  
Lipschitz Nonlinear Systems ◽  
Reference Knowledge

In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method.

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