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We deal with the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.

It is well known that more and more attention has been paid to the study of actuator saturation due to its practical and theoretical importance. Therefore, various approaches were investigated to handle systems with actuator saturation and dynamic antiwindup approach which is one of the most effective ways to deal with it. To this end, a great number of results have been reported in the literature; see, for example, [

On the other hand, Markov jump is frequently encountered in many practical systems. Therefore, the study of Markov jump systems has been a hot research topic due to its importance, and many results have been proposed based on various control techniques, such as robust control [

As it is well known, when dealing with the stability of s system, a distinction should have been made between classical Lyapunov stability and finite-time stability (FTS). Conversely, a system is said to be finite-time stable if, once we fix a time-interval, its state does not exceed some bounds during this time-interval. Some results on FTS have been carried out; see, [

In this paper, the attention is focused on the finite-time

Consider the following discrete-time Markov jump system

The unconstrained closed-loop system (

In the presence of actuator saturation, the relation between

The closed-loop systems with input saturation.

The external disturbance

The resulting closed-loop system (

The resulting closed-loop system (

In this section, we investigate the stabilization analysis of the unconstrained systems and the antiwindup controller design of the resulting closed-loop system. Some sufficient conditions in terms of LMI are given. Before presenting the main results, we give some lemmas as follows.

For the closed-loop systems (

For the given symmetric matrix

In this section, we design the controller for the unconstrained systems with

For each

Define the following Lyapunov function for each

This completes the proof.

For each

Define the following Lyapunov function for each

Based on Lemma

For each

Choose the similar Lyapunov function as Theorem

Since

In this section, a numerical example is provided to demonstrate the effectiveness of the proposed method. Consider the following systems with four operation modes.

Mode 1 is

Based on Theorem

Figures

In this paper, the finite-time

The authors declare no conflict of interests.

This work was supported by the National Natural Science Foundation of China under Grant 61203047, the Natural Science Foundation of Anhui Province under Grant 1308085QF119, the Key Foundation of Natural Science for Colleges and Universities in Anhui province under Grant KJ2012A049.