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This paper is concerned with the problem of finite-time

Positive systems are dynamical systems where the states and outputs are constrained to be nonnegative whenever the initial conditions and inputs are nonnegative [

The delta operator, as a novel method of solving the problem of system instability under fast sampling, has drawn considerable attention in the past three decades. As we know, most discrete-time signals and systems are the results of sampling continuous-time signals and systems. When the sampling period tends to zero, namely, data are taken at high sampling rates, however, all resulting signals and systems tend to be ill-conditioned and thus difficult to deal with using the conventional algorithms. Until Goodwin et al. proposed a delta-operator-based algorithm in [

The stability of positive switched systems has been concerned by many researchers [

In this paper, we focus our attention on investigating the problem of finite-time

The remainder of the paper is organized as follows. The problem formulation and some necessary lemmas are provided in Section

Consider the following switched delta operator system with time-varying delay:

Since a delta operator system can be regarded as a quasicontinuous system when

System (

System (

From the definition of delta operator

When

For any switching signal

Without lose of generality, we choose

In order to obtain the main results, we need to give the definitions of finite-time stability, finite-time boundedness and

For a given time constant

As can be seen from Definition

For a given time constant

For a given time constant

Positive switched delta operator system (

Under zero-initial condition, that is,

where

In Definition

The aim of this paper is to find a class of switching signals

This section will focus on the problem of finite-time boundedness for positive switched delta operator system (

Consider positive system (

Choose the following piecewise copositive type Lyapunov functional for positive system (

For simplicity,

Along the state decay of positive system (

Let

According to Definition

The proof is completed.

It should be noted that there is no requirement of negative definitiveness on

When

When

Consider positive system (

As stated in [

When the sampling period

Let

Consider positive system (

In this section, we will consider the problem of

Consider positive system (

Equation (

Let

Noticing that

Setting

The proof is completed.

In this section, we are interested in designing a state feedback controller

Consider positive system (

Denote

The proof is completed.

Based on Theorem

Consider positive switched delta operator system (

subsystem 1:

subsystem 2:

Choosing

Obviously, condition (

Switching signal.

State response of the closed-loop system.

State feedback control law

The evolution of

It is easy to see from Figures

In this paper, finite-time boundedness and

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China under Grant no. 61273120.