クラスのインスタンス変数をグローバル変数と同じように使えるように、PythonのSingletonパターンで作成してみます。

singleton01.py

class MySingleton(object):
    __obj = None
    __init_flg = True

    def __new__(cls, *args, **kwargs):
        if cls.__obj is None:
            cls.__obj = super().__new__(cls, *args)
        return cls.__obj

    def __init__(self):
        if self.__init_flg:
            self._x = 0
            self.__init_flg = False  # ２回目以後初期化されないように

    @property
    def x(self):
        return self._x

    @x.setter
    def x(self, value):
        self._x = value


def use_singleton1():
    print('↓--------use_singleton1')
    a1 = MySingleton()
    print('MySingleton(a1) property x = {}'.format(a1.x))
    a1.x = 150
    print('MySingleton(a1) property x = {}'.format(a1.x))
    print(a1)


def use_singleton2():
    print('↓--------use_singleton2')
    b1 = MySingleton()
    print('MySingleton(b1) property x = {}'.format(b1.x))
    b1.x = 250
    print('MySingleton(b1) property x = {}'.format(b1.x))
    print(b1)


use_singleton1()
use_singleton2()

実行結果：
↓--------use_singleton1
MySingleton(a1) property x = 0
MySingleton(a1) property x = 150
<__main__.MySingleton object at 0x00000000010C22B0>
↓--------use_singleton2
MySingleton(b1) property x = 150
MySingleton(b1) property x = 250
<__main__.MySingleton object at 0x00000000010C22B0>

複数シングルトンパターンクラスを作成するには@デコレータ関数を利用すれば便利かもしれません

singleton02.py

def singleton(cls, *args, **kwargs):
    obj = None

    def wrapper():
        nonlocal obj
        if obj is None:
            obj = cls(*args, **kwargs)
        return obj
    return wrapper

@singleton
class MySingleton(object):
    __init_flg = True

    def __init__(self):
        if self.__init_flg:
            self._x = 0
            self.__init_flg = False  # ２回目以後初期化されないように

    @property
    def x(self):
        return self._x

    @x.setter
    def x(self, value):
        self._x = value

@singleton
class MySingleton2(object):
    pass


a = MySingleton()
a.x = 11
b = MySingleton()
print('MySingleton(b) property x = {}'.format(b.x))
b.x = 12
print('MySingleton(a) property x = {}'.format(a.x))
print('MySingleton(b) property x = {}'.format(b.x))
print(a)
print(b)
print('----------------------------------------------------------')
a2 = MySingleton2()
b2 = MySingleton2()
print(a2)
print(b2)

実行結果：
MySingleton(b) property x = 11
MySingleton(a) property x = 12
MySingleton(b) property x = 12
<__main__.MySingleton object at 0x0000000000B820B8>
<__main__.MySingleton object at 0x0000000000B820B8>
----------------------------------------------------------
<__main__.MySingleton2 object at 0x0000000000B821D0>
<__main__.MySingleton2 object at 0x0000000000B821D0>

※マルチスレッドの場合、[import threading]で排他制御する必要があります