如何覆盖Flutter TabBar选项卡以用作FloatingActionButton？

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: AppBar(
          title: Text('TabBar with FloatingActionButton'),
        ),
        body: TabBarWithFab(),
      ),
    );
  }
}

class TabBarWithFab extends StatefulWidget {
  @override
  _TabBarWithFabState createState() => _TabBarWithFabState();
}

class _TabBarWithFabState extends State<TabBarWithFab>
    with SingleTickerProviderStateMixin {
  TabController _tabController;

  @override
  void initState() {
    super.initState();
    _tabController = TabController(length: 3, vsync: this);
  }

  @override
  void dispose() {
    _tabController.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return Stack(
      children: [
        TabBarView(
          controller: _tabController,
          children: [
            Container(
              color: Colors.red,
            ),
            Container(
              color: Colors.green,
            ),
            Container(
              color: Colors.blue,
            ),
          ],
        ),
        Align(
          alignment: Alignment.bottomCenter,
          child: Padding(
            padding: const EdgeInsets.only(bottom: 16.0),
            child: FloatingActionButton(
              onPressed: () {},
              child: Icon(Icons.add),
            ),
          ),
        ),
        Align(
          alignment: Alignment.bottomCenter,
          child: TabBar(
            controller: _tabController,
            tabs: [
              Tab(icon: Icon(Icons.home)),
              Tab(icon: Icon(Icons.search)),
              Tab(icon: Icon(Icons.person)),
            ],
          ),
        ),
      ],
    );
  }
}