Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

Abstract

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

Optimal Sliding Mode Preview Repetitive Control for Three-Phase Z-Source Inverters

“…Incorporating the preview controller can improve the tracking ability of the system and significantly optimize the performance of the controller [20,21]. e finite time bounded tracking control for linear continuous time-delay systems is analyzed in a reference [22]. In reference [23], the Lomberg state observer of linear discrete-time system with preview information is applied to the preview control system.…”

Finite-Time Bounded Tracking Control for Fractional-Order Systems

“…In some tracking problems, scholars sometimes desire that the output of system can always remain within the specified neighborhood of the desired tracking signal in a finite time. For instance, the robot is expected to move along the planned path in a given period of time [28]. In view of this, the concept of finite-time bounded tracking, which reflects the characteristic that the output within a given threshold of the desired tracking signal in a finite time, is proposed in [28][29].…”

“…For instance, the robot is expected to move along the planned path in a given period of time [28]. In view of this, the concept of finite-time bounded tracking, which reflects the characteristic that the output within a given threshold of the desired tracking signal in a finite time, is proposed in [28][29]. However, to our knowledge, the research on the finite-time bounded tracking still stays in the ordinary integer-order system.…”