mainwindow.cpp

#include "mainwindow.h"
#include "ui_mainwindow.h"

#include <QProcess>
MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent),
    ui(new Ui::MainWindow)
{
    this->process = new QProcess(this);
    ui->setupUi(this);

}

MainWindow::~MainWindow()
{
    delete ui;
}

void MainWindow::on_pushButton_clicked()
{

    QString program = "gnome-terminal -x sh -c 'make clean; make; ./PSE; exec bash'";
    this->process->startDetached(program);
    process->waitForFinished();

}

mainwindow.h

#ifndef MAINWINDOW_H
#define MAINWINDOW_H

#include <QMainWindow>
#include <QProcess>

namespace Ui {
class MainWindow;
}

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    explicit MainWindow(QWidget *parent = 0);
    ~MainWindow();

private slots:
    void on_pushButton_clicked();

private:
    Ui::MainWindow *ui;
    QProcess *process;
};

#endif // MAINWINDOW_H